diff --git a/changelog.d/+cooled-prek-run-env.bugfix.md b/changelog.d/+cooled-prek-run-env.bugfix.md
new file mode 100644
index 0000000..a78f406
--- /dev/null
+++ b/changelog.d/+cooled-prek-run-env.bugfix.md
@@ -0,0 +1,2 @@
+`cooled-prek` builds hook environments under the seven-day cutoff, then runs the hooks with the caller's environment, so
+a system hook that calls `uv run` resolves the project from its own lock instead of under the cutoff.
diff --git a/tests/cooled_prek/test_cooled_prek.py b/tests/cooled_prek/test_cooled_prek.py
index 72a8dac..ae2bb30 100644
--- a/tests/cooled_prek/test_cooled_prek.py
+++ b/tests/cooled_prek/test_cooled_prek.py
@@ -68,27 +68,49 @@ def test_cooled_prek_action_passes_each_argument(tmp_path: Path, action_scripts:
     ]
 
 
-def test_cooled_prek_isolates_hook_installs(tmp_path: Path) -> None:
+@pytest.mark.parametrize(
+    ("arguments", "install"),
+    [
+        pytest.param(["run", "--all-files"], ["install-hooks"], id="every-hook"),
+        pytest.param(["run", "mdformat", "--files", "CHANGELOG.md"], ["install-hooks", "mdformat"], id="named-hook"),
+    ],
+)
+def test_cooled_prek_builds_hooks_cooled_and_runs_them_with_the_caller_environment(
+    tmp_path: Path, arguments: list[str], install: list[str]
+) -> None:
     fake = tmp_path / "prek"
-    fake.write_text('#!/bin/sh\nprintf "%s\\n" "$@" >args\nenv >env\n')
+    fake.write_text(
+        '#!/bin/sh\nn=$(ls calls 2>/dev/null | wc -l)\nmkdir -p calls/$n\nprintf "%s\\n" "$@" >calls/$n/args\nenv >calls/$n/env\n'
+    )
     fake.chmod(0o755)
     leaked = dict.fromkeys(("UV_INDEX_URL", "UV_EXCLUDE_NEWER_PACKAGE", "UV_SYSTEM_CERTS", "SSL_CERT_FILE"), "leak")
 
     subprocess.run(
-        [str(Path(__file__).resolve().parents[2] / "tools/cooled_prek.sh"), "run", "--all-files"],
+        [str(Path(__file__).resolve().parents[2] / "tools/cooled_prek.sh"), *arguments],
         cwd=tmp_path,
         env=os.environ | leaked | {"PATH": f"{tmp_path}:{os.environ['PATH']}", "UV_EXCLUDE_NEWER": "1 day"},
         check=True,
     )
 
-    assert (tmp_path / "args").read_text().splitlines() == ["--config", ".pre-commit-config.yaml", "run", "--all-files"]
-    environment = dict(line.split("=", 1) for line in (tmp_path / "env").read_text().splitlines() if "=" in line)
-    assert {name: environment.get(name) for name in ("UV_EXCLUDE_NEWER", "UV_NO_CONFIG", "UV_NO_SOURCES")} == {
+    calls = [
+        (
+            (call / "args").read_text().splitlines(),
+            dict(line.split("=", 1) for line in (call / "env").read_text().splitlines() if "=" in line),
+        )
+        for call in sorted((tmp_path / "calls").iterdir(), key=lambda path: int(path.name))
+    ]
+    (install_args, install_env), (run_args, run_env) = calls
+    assert install_args == ["--config", ".pre-commit-config.yaml", *install]
+    assert {name: install_env.get(name) for name in ("UV_EXCLUDE_NEWER", "UV_NO_CONFIG", "UV_NO_SOURCES")} == {
         "UV_EXCLUDE_NEWER": "7 days",
         "UV_NO_CONFIG": "1",
         "UV_NO_SOURCES": "1",
     }
-    assert not leaked.keys() & environment.keys()
+    assert not leaked.keys() & install_env.keys()
+    assert run_args == ["--config", ".pre-commit-config.yaml", *arguments]
+    assert run_env.get("UV_EXCLUDE_NEWER") == "1 day"
+    assert "UV_NO_CONFIG" not in run_env
+    assert leaked.items() <= run_env.items()
 
 
 def test_cooled_prek_admits_nab_cutoff_exceptions(tmp_path: Path) -> None:
diff --git a/tools/cooled_prek.sh b/tools/cooled_prek.sh
index 0627d7b..f2bac0b 100755
--- a/tools/cooled_prek.sh
+++ b/tools/cooled_prek.sh
@@ -1,14 +1,16 @@
 #!/usr/bin/env bash
-# Hook environments build from PyPI under the seven-day cutoff, ignoring the repository's uv settings.
+# Hook environments build from PyPI under the seven-day cutoff, ignoring the repository's uv settings. A run then
+# executes the hooks with the caller's environment, so a system hook that calls uv resolves the project as usual.
 set -euo pipefail
-unset UV_CONFIG_FILE UV_INDEX UV_INDEX_URL UV_DEFAULT_INDEX UV_EXTRA_INDEX_URL
-unset UV_FIND_LINKS UV_EXCLUDE_NEWER_PACKAGE
-unset UV_INSECURE_HOST UV_SYSTEM_CERTS SSL_CERT_FILE SSL_CERT_DIR
-export UV_EXCLUDE_NEWER="7 days" UV_NO_CONFIG=1 UV_NO_SOURCES=1
-# uv pip, which prek calls, reads per-package cutoffs only from a config file, so the [tool.nab] exceptions the
-# release lock already admits are written to one that holds nothing else.
-exceptions=$(
-  python3 -I - <<'PY'
+cooled() (
+  unset UV_CONFIG_FILE UV_INDEX UV_INDEX_URL UV_DEFAULT_INDEX UV_EXTRA_INDEX_URL
+  unset UV_FIND_LINKS UV_EXCLUDE_NEWER_PACKAGE
+  unset UV_INSECURE_HOST UV_SYSTEM_CERTS SSL_CERT_FILE SSL_CERT_DIR
+  export UV_EXCLUDE_NEWER="7 days" UV_NO_CONFIG=1 UV_NO_SOURCES=1
+  # uv pip, which prek calls, reads per-package cutoffs only from a config file, so the [tool.nab] exceptions the
+  # release lock already admits are written to one that holds nothing else.
+  exceptions=$(
+    python3 -I - <<'PY'
 import pathlib
 import tomllib
 
@@ -19,14 +21,28 @@ for name, settings in sorted(packages.items()):
         value = cutoff.isoformat().replace("+00:00", "Z") if hasattr(cutoff, "isoformat") else str(cutoff)
         print(f'"{name}" = "{value}"')
 PY
+  )
+  if [[ -n "$exceptions" ]]; then
+    config=$(mktemp)
+    printf '[exclude-newer-package]\n%s\n' "$exceptions" >"$config"
+    export UV_CONFIG_FILE="$config"
+    echo "Running prek $* with hook environments built under the 7 days cutoff, repository uv settings ignored," \
+      "[tool.nab] cutoff exceptions admitted: $(tr '\n' ' ' <<<"$exceptions")"
+  else
+    echo "Running prek $* with hook environments built under the 7 days cutoff, repository uv settings ignored"
+  fi
+  exec prek --config .pre-commit-config.yaml "$@"
 )
-if [[ -n "$exceptions" ]]; then
-  config=$(mktemp)
-  printf '[exclude-newer-package]\n%s\n' "$exceptions" >"$config"
-  export UV_CONFIG_FILE="$config"
-  echo "Running prek $* with hook environments built under the 7 days cutoff, repository uv settings ignored," \
-    "[tool.nab] cutoff exceptions admitted: $(tr '\n' ' ' <<<"$exceptions")"
-else
-  echo "Running prek $* with hook environments built under the 7 days cutoff, repository uv settings ignored"
+if [[ "${1:-}" != run ]]; then
+  cooled "$@"
+  exit
 fi
+# The hook IDs a run names come before its first option; none means every hook.
+hooks=()
+for argument in "${@:2}"; do
+  [[ "$argument" == -* ]] && break
+  hooks+=("$argument")
+done
+cooled install-hooks ${hooks[@]+"${hooks[@]}"}
+echo "Running prek $* with the caller's environment"
 exec prek --config .pre-commit-config.yaml "$@"