Index: Lib/tempfile.py
===================================================================
--- Lib/tempfile.py	(revision 87169)
+++ Lib/tempfile.py	(working copy)
@@ -29,6 +29,8 @@
 
 # Imports.
 
+import warnings as _warnings
+import sys as _sys
 import io as _io
 import os as _os
 import errno as _errno
@@ -617,23 +619,41 @@
     """
 
     def __init__(self, suffix="", prefix=template, dir=None):
+        self._closed = False
+        self.name = None # Handle mkdtemp throwing an exception
         self.name = mkdtemp(suffix, prefix, dir)
-        self._closed = False
 
+    def __repr__(self):
+        return "<{} {!r}>".format(self.__class__.__name__, self.name)
+
     def __enter__(self):
         return self.name
 
-    def cleanup(self):
-        if not self._closed:
-            self._rmtree(self.name)
+    def cleanup(self, _warn=False):
+        if self.name and not self._closed:
+            try:
+                self._rmtree(self.name)
+            except (TypeError, AttributeError) as ex:
+                # Issue 10888: Emit a warning on stderr
+                # if the directory could not be cleaned
+                # up due to missing globals
+                if "None" not in str(ex):
+                    raise
+                print("ERROR: {!r} while cleaning up {!r}".format(ex, self,),
+                      file=_sys.stderr)
+                return
             self._closed = True
+            if _warn:
+                self._warn("Implicitly cleaning up {!r}".format(self),
+                           ResourceWarning)
 
     def __exit__(self, exc, value, tb):
         self.cleanup()
 
-    __del__ = cleanup
+    def __del__(self):
+        # Issue a ResourceWarning if implicit cleanup needed
+        self.cleanup(_warn=True)
 
-
     # XXX (ncoghlan): The following code attempts to make
     # this class tolerant of the module nulling out process
     # that happens during CPython interpreter shutdown
@@ -644,6 +664,7 @@
     _remove = staticmethod(_os.remove)
     _rmdir = staticmethod(_os.rmdir)
     _os_error = _os.error
+    _warn = _warnings.warn
 
     def _rmtree(self, path):
         # Essentially a stripped down version of shutil.rmtree.  We can't
Index: Lib/test/test_tempfile.py
===================================================================
--- Lib/test/test_tempfile.py	(revision 87169)
+++ Lib/test/test_tempfile.py	(working copy)
@@ -925,6 +925,13 @@
             f.write(b"Hello world!")
         return tmp
 
+    def test_mkdtemp_failure(self):
+        # Check no additional exception if mkdtemp fails
+        # Previously would raise AttributeError instead
+        # (noted as part of Issue #10888)
+        #with self.assertRaises(os.error):
+            tempfile.TemporaryDirectory(prefix="[]<>?*!:")
+
     def test_explicit_cleanup(self):
         # A TemporaryDirectory is deleted when cleaned up
         dir = tempfile.mkdtemp()
@@ -955,8 +962,7 @@
     def test_del_on_shutdown(self):
         # A TemporaryDirectory may be cleaned up during shutdown
         # Make sure it works with the relevant modules nulled out
-        dir = tempfile.mkdtemp()
-        try:
+        with self.do_create() as dir:
             d = self.do_create(dir=dir)
             # Mimic the nulling out of modules that
             # occurs during system shutdown
@@ -967,9 +973,32 @@
                 d.cleanup()
             self.assertFalse(os.path.exists(d.name),
                         "TemporaryDirectory %s exists after cleanup" % d.name)
-        finally:
-            os.rmdir(dir)
 
+    def test_warnings_on_cleanup(self):
+        # Two kinds of warning on shutdown
+        #   Issue 10888: may write to stderr if modules are nulled out
+        #   ResourceWarning will be triggered by __del__
+        with self.do_create() as dir:
+            d = self.do_create(dir=dir)
+
+            #Check for the Issue 10888 message
+            modules = [os, os.path]
+            if has_stat:
+                modules.append(stat)
+            with support.captured_stderr() as err:
+                with NulledModules(*modules):
+                    d.cleanup()
+            message = err.getvalue()
+            self.assertIn("while cleaning up",  message)
+            self.assertIn(d.name,  message)
+
+            # Check for the resource warning
+            with support.check_warnings(('Implicitly', ResourceWarning), quiet=False):
+                warnings.filterwarnings("always", category=ResourceWarning)
+                d.__del__()
+            self.assertFalse(os.path.exists(d.name),
+                        "TemporaryDirectory %s exists after __del__" % d.name)
+
     def test_multiple_close(self):
         # Can be cleaned-up many times without error
         d = self.do_create()
Index: Lib/test/support.py
===================================================================
--- Lib/test/support.py	(revision 87169)
+++ Lib/test/support.py	(working copy)
@@ -874,6 +874,9 @@
 def captured_stdout():
     return captured_output("stdout")
 
+def captured_stderr():
+    return captured_output("stderr")
+
 def captured_stdin():
     return captured_output("stdin")