diff --git a/Lib/tempfile.py b/Lib/tempfile.py
index 3e1e08dba21..8ac707d7e09 100644
--- a/Lib/tempfile.py
+++ b/Lib/tempfile.py
@@ -67,25 +67,40 @@ def gettempdir():
     return tempdir
 
 
-_pid = None
+# template caches the result of gettempprefix, for speed, when possible.
+# XXX unclear why this isn't "_template"; left it "template" for backward
+# compatibility.
+if os.name == "posix":
+    # We don't try to cache the template on posix:  the pid may change on us
+    # between calls due to a fork, and on Linux the pid changes even for
+    # another thread in the same process.  Since any attempt to keep the
+    # cache in synch would have to call os.getpid() anyway in order to make
+    # sure the pid hasn't changed between calls, a cache wouldn't save any
+    # time.  In addition, a cache is difficult to keep correct with the pid
+    # changing willy-nilly, and earlier attempts proved buggy (races).
+    template = None
+
+# Else the pid never changes, so gettempprefix always returns the same
+# string.
+elif os.name == "nt":
+    template = '~' + `os.getpid()` + '-'
+elif os.name == 'mac':
+    template = 'Python-Tmp-'
+else:
+    template = 'tmp' # XXX might choose a better one
 
 def gettempprefix():
-    """Function to calculate a prefix of the filename to use."""
-    global template, _pid
-    if os.name == 'posix' and _pid and _pid != os.getpid():
-        # Our pid changed; we must have forked -- zap the template
-        template = None
+    """Function to calculate a prefix of the filename to use.
+
+    This incorporates the current process id on systems that support such a
+    notion, so that concurrent processes don't generate the same prefix.
+    """
+
+    global template
     if template is None:
-        if os.name == 'posix':
-            _pid = os.getpid()
-            template = '@' + `_pid` + '.'
-        elif os.name == 'nt':
-            template = '~' + `os.getpid()` + '-'
-        elif os.name == 'mac':
-            template = 'Python-Tmp-'
-        else:
-            template = 'tmp' # XXX might choose a better one
-    return template
+        return '@' + `os.getpid()` + '.'
+    else:
+        return template
 
 
 def mktemp(suffix=""):
diff --git a/Lib/test/output/test_threadedtempfile b/Lib/test/output/test_threadedtempfile
new file mode 100644
index 00000000000..2552877a398
--- /dev/null
+++ b/Lib/test/output/test_threadedtempfile
@@ -0,0 +1,5 @@
+test_threadedtempfile
+Creating
+Starting
+Reaping
+Done: errors 0 ok 1000
diff --git a/Lib/test/test_threadedtempfile.py b/Lib/test/test_threadedtempfile.py
new file mode 100644
index 00000000000..a5ee12f59bd
--- /dev/null
+++ b/Lib/test/test_threadedtempfile.py
@@ -0,0 +1,85 @@
+"""
+Create and delete FILES_PER_THREAD temp files (via tempfile.TemporaryFile)
+in each of NUM_THREADS threads, recording the number of successes and
+failures.  A failure is a bug in tempfile, and may be due to:
+
++ Trying to create more than one tempfile with the same name.
++ Trying to delete a tempfile that doesn't still exist.
++ Something we've never seen before.
+
+By default, NUM_THREADS == 20 and FILES_PER_THREAD == 50.  This is enough to
+create about 150 failures per run under Win98SE in 2.0, and runs pretty
+quickly. Guido reports needing to boost FILES_PER_THREAD to 500 before
+provoking a 2.0 failure under Linux.  Run the test alone to boost either
+via cmdline switches:
+
+-f  FILES_PER_THREAD (int)
+-t  NUM_THREADS (int)
+"""
+
+NUM_THREADS = 20        # change w/ -t option
+FILES_PER_THREAD = 50   # change w/ -f option
+
+import threading
+from test.test_support import TestFailed
+import StringIO
+from traceback import print_exc
+
+startEvent = threading.Event()
+
+import tempfile
+tempfile.gettempdir() # Do this now, to avoid spurious races later
+
+class TempFileGreedy(threading.Thread):
+    error_count = 0
+    ok_count = 0
+
+    def run(self):
+        self.errors = StringIO.StringIO()
+        startEvent.wait()
+        for i in range(FILES_PER_THREAD):
+            try:
+                f = tempfile.TemporaryFile("w+b")
+                f.close()
+            except:
+                self.error_count += 1
+                print_exc(file=self.errors)
+            else:
+                self.ok_count += 1
+
+def _test():
+    threads = []
+
+    print "Creating"
+    for i in range(NUM_THREADS):
+        t = TempFileGreedy()
+        threads.append(t)
+        t.start()
+
+    print "Starting"
+    startEvent.set()
+
+    print "Reaping"
+    ok = errors = 0
+    for t in threads:
+        t.join()
+        ok += t.ok_count
+        errors += t.error_count
+        if t.error_count:
+            print '%s errors:\n%s' % (t.getName(), t.errors.getvalue())
+
+    msg = "Done: errors %d ok %d" % (errors, ok)
+    print msg
+    if errors:
+        raise TestFailed(msg)
+
+if __name__ == "__main__":
+    import sys, getopt
+    opts, args = getopt.getopt(sys.argv[1:], "t:f:")
+    for o, v in opts:
+        if o == "-f":
+            FILES_PER_THREAD = int(v)
+        elif o == "-t":
+            NUM_THREADS = int(v)
+
+_test()