diff --git a/Lib/tempfile.py b/Lib/tempfile.py
index cbaac43..7e03784 100644
--- a/Lib/tempfile.py
+++ b/Lib/tempfile.py
@@ -617,6 +617,8 @@
     """
 
     def __init__(self, suffix="", prefix=template, dir=None):
+        # cleanup() needs this and is called even when mkdtemp fails
+        self._closed = True
         self.name = mkdtemp(suffix, prefix, dir)
         self._closed = False