diff --git a/deploy/beta/env.beta.template b/deploy/beta/env.beta.template
index 8a2f7e26..13e11b5f 100644
--- a/deploy/beta/env.beta.template
+++ b/deploy/beta/env.beta.template
@@ -22,4 +22,12 @@ CHAINLIT_URL=https://beta.reactome.org
 # anything else makes retrieval meaningless.
 #EMBEDDING_MODEL=
 # LLM used for answers; defaults to gpt-4o-mini.
+# gpt-5.6-luna is verified to work end to end. It answers with noticeably more
+# grounding in the retrieved Reactome records, and takes roughly twice as long
+# per question (41s vs 22s, averaged over three questions).
 #LLM_MODEL=
+# Sampling temperature. Leave unset: it defaults to 0.0, except for the
+# gpt-5.5/5.6/6 families, which accept only their own default of 1 and return a
+# 400 for anything else. Set this only for a model that rule does not yet know
+# about; see resolve_temperature in src/agent/graph.py.
+#LLM_TEMPERATURE=
diff --git a/env_template b/env_template
index e0963807..a7343c9e 100644
--- a/env_template
+++ b/env_template
@@ -20,4 +20,12 @@ TAVILY_API_KEY=
 # anything else makes retrieval meaningless.
 #EMBEDDING_MODEL=
 # LLM used for answers; defaults to gpt-4o-mini.
+# gpt-5.6-luna is verified to work end to end. It answers with noticeably more
+# grounding in the retrieved Reactome records, and takes roughly twice as long
+# per question (41s vs 22s, averaged over three questions).
 #LLM_MODEL=
+# Sampling temperature. Leave unset: it defaults to 0.0, except for the
+# gpt-5.5/5.6/6 families, which accept only their own default of 1 and return a
+# 400 for anything else. Set this only for a model that rule does not yet know
+# about; see resolve_temperature in src/agent/graph.py.
+#LLM_TEMPERATURE=
diff --git a/src/agent/graph.py b/src/agent/graph.py
index 4fafd9db..4716ecdf 100644
--- a/src/agent/graph.py
+++ b/src/agent/graph.py
@@ -78,6 +78,42 @@ def resolve_embedding_model() -> str:
     return configured or bundle_model
 
 
+# Models that accept only one temperature: their own default of 1. Any other
+# value, 0.0 included, is a 400 on the first request rather than an error at
+# construction:
+#
+#   Unsupported value: 'temperature' does not support 0.0 with this model.
+#   Only the default (1) value is supported.
+#
+# Sending nothing is not an option -- ChatOpenAI supplies its own default of 0.7
+# when the argument is omitted, and these models reject that too -- so the value
+# has to be 1.0 explicitly.
+#
+# Unlike the embedding model, which is read from the bundle that built it, this
+# cannot be derived: no endpoint reports which values a model accepts. Matched on
+# prefix so dated snapshots (gpt-5.5-2026-04-23) and new members of a family
+# need no edit. LLM_TEMPERATURE overrides, for a model this list has not met.
+FIXED_TEMPERATURE_MODEL_PREFIXES = ("gpt-5.5", "gpt-5.6", "gpt-6")
+FIXED_TEMPERATURE = 1.0
+
+
+def resolve_temperature(model: str) -> float:
+    """The temperature to send for `model`.
+
+    Returning 1.0 for the models above trades determinism for being able to use
+    them at all. That trade is made here, once, rather than at each call site.
+    """
+    override = os.getenv("LLM_TEMPERATURE")
+    if override is not None and override.strip() != "":
+        try:
+            return float(override)
+        except ValueError:
+            raise SystemExit(f"LLM_TEMPERATURE={override!r} is not a number.") from None
+    if model.startswith(FIXED_TEMPERATURE_MODEL_PREFIXES):
+        return FIXED_TEMPERATURE
+    return 0.0
+
+
 class AgentGraph:
     def __init__(
         self,
@@ -88,7 +124,11 @@ def __init__(
         llm_model = os.getenv("LLM_MODEL", "gpt-4o-mini")
         llm_base_url = os.getenv("LLM_BASE_URL", None)
         llm: BaseChatModel = get_llm(
-            "openai", llm_model, base_url=llm_base_url, request_timeout=360.0
+            "openai",
+            llm_model,
+            base_url=llm_base_url,
+            request_timeout=360.0,
+            temperature=resolve_temperature(llm_model),
         )
         embedding_base_url = os.getenv("OPENAI_BASE_URL", None)
         embedding: Embeddings = get_embedding(
diff --git a/src/agent/models.py b/src/agent/models.py
index 904ca3e4..cf7f74c9 100644
--- a/src/agent/models.py
+++ b/src/agent/models.py
@@ -49,20 +49,33 @@ def get_llm(
     *,
     base_url: str | None = None,
     request_timeout: float | None = None,
+    temperature: float = 0.0,
 ) -> BaseChatModel:
+    """Build a chat model. See `agent.graph.resolve_temperature` for the value.
+
+    0.0 is what this repository wants everywhere -- the graders, the intent
+    classifier and the query expander should all give the same answer twice.
+    Some models refuse it, which is why this is a parameter rather than the
+    constant it used to be.
+
+    There is no way to send *no* temperature on langchain-openai 0.2.14:
+    omitting the argument makes ChatOpenAI send its own pydantic default of 0.7,
+    which the models that refuse 0.0 refuse just as firmly. So the caller must
+    pass a value the model accepts; it cannot opt out.
+    """
     if model is None:
         provider, model = provider.split("/", 1)
     if provider == "openai":
         return ChatOpenAI(
             model=model,
-            temperature=0.0,
+            temperature=temperature,
             base_url=base_url,
             request_timeout=request_timeout,  # type: ignore[call-arg]  # pydantic-generated __init__
         )
     if provider == "ollama":
         return ChatOllama(
             model=model,
-            temperature=0.0,
+            temperature=temperature,
             base_url=base_url,
             request_timeout=request_timeout,  # type: ignore[call-arg]  # pydantic-generated __init__
         )
diff --git a/src/agent/tasks/completeness_grader.py b/src/agent/tasks/completeness_grader.py
index e2254ac8..264c3717 100644
--- a/src/agent/tasks/completeness_grader.py
+++ b/src/agent/tasks/completeness_grader.py
@@ -28,5 +28,13 @@ class CompletenessGrade(BaseModel):
     )
 
 
+# json_schema, not the default function_calling: the gpt-5.6 family refuses
+# function tools on /v1/chat/completions ("Function tools with reasoning_effort
+# are not supported ... use /v1/responses or set reasoning_effort to 'none'"),
+# and langchain-openai 0.2.14 has no Responses API support. json_schema uses
+# response_format instead, which every model here accepts -- verified against
+# gpt-4o-mini and gpt-5.6-luna for all three graders.
 def create_completeness_grader(llm: BaseChatModel) -> Runnable:
-    return completeness_prompt | llm.with_structured_output(CompletenessGrade)
+    return completeness_prompt | llm.with_structured_output(
+        CompletenessGrade, method="json_schema"
+    )
diff --git a/src/agent/tasks/intent_classifier.py b/src/agent/tasks/intent_classifier.py
index 17aa2b0f..bf1d72bc 100644
--- a/src/agent/tasks/intent_classifier.py
+++ b/src/agent/tasks/intent_classifier.py
@@ -57,5 +57,13 @@ def resolve_active_sources(
     return [next(iter(available_sources))]
 
 
+# json_schema, not the default function_calling: the gpt-5.6 family refuses
+# function tools on /v1/chat/completions ("Function tools with reasoning_effort
+# are not supported ... use /v1/responses or set reasoning_effort to 'none'"),
+# and langchain-openai 0.2.14 has no Responses API support. json_schema uses
+# response_format instead, which every model here accepts -- verified against
+# gpt-4o-mini and gpt-5.6-luna for all three graders.
 def create_intent_classifier(llm: BaseChatModel) -> Runnable:
-    return intent_classifier_prompt | llm.with_structured_output(QueryIntent)
+    return intent_classifier_prompt | llm.with_structured_output(
+        QueryIntent, method="json_schema"
+    )
diff --git a/src/agent/tasks/safety_checker.py b/src/agent/tasks/safety_checker.py
index c1360133..f69fcadb 100644
--- a/src/agent/tasks/safety_checker.py
+++ b/src/agent/tasks/safety_checker.py
@@ -69,5 +69,13 @@ class SafetyCheck(BaseModel):
     )
 
 
+# json_schema, not the default function_calling: the gpt-5.6 family refuses
+# function tools on /v1/chat/completions ("Function tools with reasoning_effort
+# are not supported ... use /v1/responses or set reasoning_effort to 'none'"),
+# and langchain-openai 0.2.14 has no Responses API support. json_schema uses
+# response_format instead, which every model here accepts -- verified against
+# gpt-4o-mini and gpt-5.6-luna for all three graders.
 def create_safety_checker(llm: BaseChatModel) -> Runnable:
-    return safety_check_prompt | llm.with_structured_output(SafetyCheck)
+    return safety_check_prompt | llm.with_structured_output(
+        SafetyCheck, method="json_schema"
+    )
diff --git a/tests/agent/test_model_temperature.py b/tests/agent/test_model_temperature.py
new file mode 100644
index 00000000..33aa2493
--- /dev/null
+++ b/tests/agent/test_model_temperature.py
@@ -0,0 +1,102 @@
+"""Which temperature gets sent, and to which models.
+
+The gpt-5.5/5.6 families and gpt-6-astra accept only their own default of 1.
+Every other value is a 400 on the *first request*, not at construction, so
+nothing catches it until a user asks a question.
+
+There is no way to send no temperature at all: omitting the argument makes
+ChatOpenAI send its own pydantic default of 0.7, which those models reject just
+as firmly as 0.0. An earlier version of this change tried exactly that, and
+`model_dump(exclude_unset=True)` agreed the field was unset -- while the request
+still carried 0.7. So the assertions below are about the value chosen, and the
+live behaviour was verified by hand against the API.
+"""
+
+import pytest
+
+pytest.importorskip("langchain_openai", reason="LLM stack not installed")
+
+from langchain_openai.chat_models.base import ChatOpenAI  # noqa: E402
+
+from agent.graph import FIXED_TEMPERATURE, resolve_temperature  # noqa: E402
+from agent.models import get_llm  # noqa: E402
+
+
+def _built(model: str, **kwargs: float) -> ChatOpenAI:
+    """get_llm is typed BaseChatModel; the temperature lives on ChatOpenAI."""
+    llm = get_llm("openai", model, **kwargs)  # type: ignore[arg-type]
+    assert isinstance(llm, ChatOpenAI)
+    return llm
+
+
+@pytest.fixture(autouse=True)
+def _no_override(monkeypatch: pytest.MonkeyPatch) -> None:
+    """A developer's LLM_TEMPERATURE must not decide what these tests assert."""
+    monkeypatch.delenv("LLM_TEMPERATURE", raising=False)
+
+
+@pytest.mark.parametrize(
+    "model",
+    ["gpt-5.5", "gpt-5.5-2026-04-23", "gpt-5.6-luna", "gpt-5.6-sol", "gpt-6-astra"],
+)
+def test_models_that_refuse_zero_get_their_only_supported_value(model: str) -> None:
+    assert resolve_temperature(model) == FIXED_TEMPERATURE == 1.0
+
+
+@pytest.mark.parametrize("model", ["gpt-4o-mini", "gpt-4.1", "gpt-5", "gpt-5.4-mini"])
+def test_every_other_model_still_gets_zero(model: str) -> None:
+    """Determinism stays the default; only the models that refuse it lose it.
+
+    gpt-5 and gpt-5.4-mini are in this list deliberately: they are newer than
+    gpt-4o-mini and they do accept 0.0, so the rule is not "new models".
+    """
+    assert resolve_temperature(model) == 0.0
+
+
+def test_the_prefix_table_covers_dated_snapshots() -> None:
+    """gpt-5.6-luna and a dated pin of it must resolve the same way.
+
+    Matching on prefix is why this table needs no edit each time OpenAI pins a
+    snapshot of a family already listed.
+    """
+    assert resolve_temperature("gpt-5.6-luna-2026-06-01") == FIXED_TEMPERATURE
+
+
+def test_the_override_wins_over_the_table(monkeypatch: pytest.MonkeyPatch) -> None:
+    """The escape hatch, for a model the table has not met."""
+    monkeypatch.setenv("LLM_TEMPERATURE", "1")
+    assert resolve_temperature("gpt-4o-mini") == 1.0
+    monkeypatch.setenv("LLM_TEMPERATURE", "0")
+    assert resolve_temperature("gpt-5.6-luna") == 0.0
+
+
+@pytest.mark.parametrize("value", ["", "   "])
+def test_an_empty_override_is_treated_as_unset(
+    value: str, monkeypatch: pytest.MonkeyPatch
+) -> None:
+    """An empty env var in a compose file means "not configured", not 0.0."""
+    monkeypatch.setenv("LLM_TEMPERATURE", value)
+    assert resolve_temperature("gpt-4o-mini") == 0.0
+
+
+def test_an_unparseable_override_stops_the_process(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """Article IV: a temperature nobody can honour must not fall back silently."""
+    monkeypatch.setenv("LLM_TEMPERATURE", "warm")
+    with pytest.raises(SystemExit, match="not a number"):
+        resolve_temperature("gpt-4o-mini")
+
+
+def test_get_llm_sends_the_temperature_it_is_given(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    monkeypatch.setenv("OPENAI_API_KEY", "sk-not-a-real-key")  # construction only
+    assert _built("gpt-4o-mini", temperature=0.0).temperature == 0.0
+    assert _built("gpt-5.6-luna", temperature=1.0).temperature == 1.0
+
+
+def test_get_llm_still_defaults_to_zero(monkeypatch: pytest.MonkeyPatch) -> None:
+    """Callers that never heard of this change keep the old behaviour."""
+    monkeypatch.setenv("OPENAI_API_KEY", "sk-not-a-real-key")
+    assert _built("gpt-4o-mini").temperature == 0.0