diff --git a/Lib/tempfile.py b/Lib/tempfile.py
index 766cc63a98a1c0d..bb0a035a4b96fcc 100644
--- a/Lib/tempfile.py
+++ b/Lib/tempfile.py
@@ -863,7 +863,7 @@ def __init__(self, suffix=None, prefix=None, dir=None,
             ignore_errors=self._ignore_cleanup_errors)
 
     @classmethod
-    def _rmtree(cls, name, ignore_errors=False):
+    def _rmtree(cls, name, ignore_errors=False, retrying=None):
         def without_following_symlinks(func, path, *args):
             # Pass follow_symlinks=False, unless not supported on this platform.
             if func in _os.supports_follow_symlinks:
@@ -889,7 +889,9 @@ def onerror(func, path, exc_info):
                         _os.unlink(path)
                     # PermissionError is raised on FreeBSD for directories
                     except (IsADirectoryError, PermissionError):
-                        cls._rmtree(path, ignore_errors=ignore_errors)
+                        if path == retrying:
+                            raise # already tried (and failed) to fix this once
+                        cls._rmtree(path, ignore_errors=ignore_errors, retrying=path)
                 except FileNotFoundError:
                     pass
             elif issubclass(exc_info[0], FileNotFoundError):
diff --git a/Lib/test/test_tempfile.py b/Lib/test/test_tempfile.py
index c022e2e0f8d1144..ab42e720964895a 100644
--- a/Lib/test/test_tempfile.py
+++ b/Lib/test/test_tempfile.py
@@ -1691,6 +1691,30 @@ def patched_unlink(path, **kwargs):
                          "Mode of the directory pointed to by a symlink changed")
         d2.cleanup()
 
+    def test_cleanup_with_error_deleting_directory(self):
+        # cleanup() should not recurse infinitely on PermissionError when deleting directory
+        d = self.do_create()
+
+        # There are a variety of reasons why the OS may raise a PermissionError,
+        # but provoking those reliably and cross-platform is not straightforward,
+        # so raise the error synthetically instead.
+        real_rmdir = os.rmdir
+        error_was_raised = False
+        def patched_rmdir(path, **kwargs):
+            nonlocal error_was_raised
+            # rmdir may be called with full path or path relative to 'fd' kwarg.
+            if path.endswith("dir0"):
+                error_was_raised = True
+                raise PermissionError()
+            real_rmdir(path, **kwargs)
+
+        with mock.patch("tempfile._os.rmdir", patched_rmdir):
+            # This call to cleanup() should fail with PermissionError, not recurse infinitely.
+            self.assertRaises(PermissionError, d.cleanup)
+
+        self.assertTrue(error_was_raised, "did not see expected 'rmdir' call")
+        d.cleanup()
+
     @support.cpython_only
     def test_del_on_collection(self):
         # A TemporaryDirectory is deleted when garbage collected