diff --git a/bigcode_eval/tasks/multiple.py b/bigcode_eval/tasks/multiple.py
index 875c648f1..bdf25d05c 100644
--- a/bigcode_eval/tasks/multiple.py
+++ b/bigcode_eval/tasks/multiple.py
@@ -151,8 +151,9 @@ def process_results(self, generations, references):
             for i, doc in enumerate(self.get_dataset())
             if i < len(generations)
         ]
-        # a common temp dir for all the problems
-        temp_dir = tempfile.gettempdir()
+        # a fresh temp dir for the problems of this run, so that results files
+        # left in the shared temp dir by other runs or tasks are not scored
+        temp_dir = tempfile.mkdtemp()
         list_files = []
         for (prompt_name, generation, reference) in zip(
             prompts_names, generations, references
diff --git a/tests/test_multiple.py b/tests/test_multiple.py
new file mode 100644
index 000000000..6f91c7dd7
--- /dev/null
+++ b/tests/test_multiple.py
@@ -0,0 +1,106 @@
+import json
+import os
+import tempfile
+
+import pytest
+
+from bigcode_eval.tasks import multiple
+from bigcode_eval.tasks.custom_metrics.multiple_metrics.evaluation import \
+    get_test_results_json_path
+
+NAMES = [
+    "HumanEval_0_has_close_elements",
+    "HumanEval_1_separate_paren_groups",
+    "HumanEval_2_truncate_number",
+]
+
+
+class DummyMultiPLE(multiple.GeneralMultiPLE):
+    # skips loading the dataset from the hub
+    def __init__(self, language, names):
+        self.language = language
+        self.docs = [
+            {"prompt": f"prompt {name}", "name": name, "language": language}
+            for name in names
+        ]
+
+    def get_dataset(self):
+        return self.docs
+
+
+def fake_evaluate_problem(output_dir, problem_json_path, max_workers):
+    # writes a results file in the same format as the real evaluate_problem,
+    # a completion passes when it ends with "pass"
+    with open(problem_json_path) as f:
+        problem = json.load(f)
+    results = []
+    for completion in problem["completions"]:
+        ok = completion.endswith("pass")
+        status = "OK" if ok else "Exception"
+        results.append({"status": status, "exit_code": 0 if ok else 1})
+    test_results = {"name": problem["name"], "results": results}
+    path = get_test_results_json_path(output_dir, problem_json_path, None)
+    with open(path, "w") as f:
+        json.dump(test_results, f)
+
+
+@pytest.fixture
+def system_tmp(tmp_path, monkeypatch):
+    # stand-in for the system temp dir, shared by every run on the machine
+    monkeypatch.setattr(tempfile, "tempdir", str(tmp_path))
+    monkeypatch.setattr(multiple, "evaluate_problem", fake_evaluate_problem)
+    return tmp_path
+
+
+def write_leftover(directory, name, n_ok):
+    results = [{"status": "OK", "exit_code": 0}] * n_ok
+    with open(os.path.join(directory, f"{name}.results.json"), "w") as f:
+        json.dump({"name": name, "results": results}, f)
+
+
+def run(task, generations):
+    references = ["tests"] * len(generations)
+    return task.process_results(generations, references)
+
+
+def test_single_run_mixed(system_tmp):
+    task = DummyMultiPLE("js", NAMES[:2])
+    assert run(task, [["fail"], ["pass"]]) == {"pass@1": 0.5}
+
+
+def test_single_run_all_pass_and_all_fail(system_tmp):
+    task = DummyMultiPLE("js", NAMES)
+    assert run(task, [["pass"]] * 3) == {"pass@1": 1.0}
+    assert run(task, [["fail"]] * 3) == {"pass@1": 0.0}
+
+
+def test_several_samples_per_problem(system_tmp):
+    task = DummyMultiPLE("js", NAMES[:2])
+    generations = [["pass"] * 3 + ["fail"] * 7, ["fail"] * 10]
+    results = run(task, generations)
+    assert set(results) == {"pass@1", "pass@10"}
+    assert results["pass@1"] == pytest.approx(0.15)
+    assert results["pass@10"] == pytest.approx(0.5)
+
+
+def test_leftover_results_file_is_not_scored(system_tmp):
+    write_leftover(system_tmp, "HumanEval_99_leftover", n_ok=20)
+    task = DummyMultiPLE("js", NAMES[:1])
+    assert run(task, [["fail"]]) == {"pass@1": 0.0}
+
+
+def test_leftover_results_file_is_left_alone(system_tmp):
+    write_leftover(system_tmp, "HumanEval_99_leftover", n_ok=20)
+    task = DummyMultiPLE("js", NAMES[:1])
+    run(task, [["fail"]])
+    assert os.path.exists(
+        os.path.join(system_tmp, "HumanEval_99_leftover.results.json")
+    )
+
+
+def test_previous_task_in_same_process_is_not_scored(system_tmp):
+    # problem names are shared across languages, js has more problems than d
+    js = DummyMultiPLE("js", NAMES)
+    d = DummyMultiPLE("d", NAMES[:2])
+    assert run(js, [["pass"]] * 3) == {"pass@1": 1.0}
+    assert run(d, [["fail"]] * 2) == {"pass@1": 0.0}