When an exception occurs within a tempfile.TemporaryDirectory() context
and the directory cleanup fails, the _cleanup exception_ is propagated,
not the original one. This effectively 'masks' the original exception,
and makes it impossible to catch using a simple 'try'/'except' construct.

----------------------------------------------------------------------------
Code like this:

  import tempfile
  import os
  import sys

  try:
      with tempfile.TemporaryDirectory() as tempdir:
          print(tempdir)
          # some code happens here

  except ArithmeticError as exc:
      print('An arithmetic error occurred: {}'.format(exc))

  print('Continuing...')

is effective at catching any ArithmeticError which occurs in the
code fragment but is not otherwise handled. However if, in addition,
an error occues in cleaning up the temporary directory, the exception
which occurred in the code is replaced by the cleanup exception, and is
not be propagated to be caught by the 'except' clause.

For example:

  import tempfile
  import os
  import sys

  try:
      with tempfile.TemporaryDirectory() as tempdir:
          print(tempdir)
          n = 1 / 0

  except ArithmeticError as exc:
      print('An arithmetic error occurred: {}'.format(exc))

  print('Continuing...')

produces this:

  /tmp/tmp_r2sxqgb
  An arithmetic error occurred: division by zero
  Continuing...

but this:

  import tempfile
  import os
  import sys

  try:
      with tempfile.TemporaryDirectory() as tempdir:
          print(tempdir)
          os.rmdir(tempdir)  # this new line is the only difference
          n = 1 / 0

  except ArithmeticError as exc:
      print('An arithmetic error occurred: {}'.format(exc))

  print('Continuing...')

produces this:

  /tmp/tmp_yz6zyfs
  Traceback (most recent call last):
    File "tempfilebug.py", line 9, in <module>
      n = 1 / 0
  ZeroDivisionError: division by zero

  During handling of the above exception, another exception occurred:

  Traceback (most recent call last):
    File "tempfilebug.py", line 9, in <module>
      n = 1 / 0
    File "/usr/lib/python3.6/tempfile.py", line 948, in __exit__
      self.cleanup()
    File "/usr/lib/python3.6/tempfile.py", line 952, in cleanup
      _rmtree(self.name)
    File "/usr/lib/python3.6/shutil.py", line 477, in rmtree
      onerror(os.lstat, path, sys.exc_info())
    File "/usr/lib/python3.6/shutil.py", line 475, in rmtree
      orig_st = os.lstat(path)
  FileNotFoundError: [Errno 2] No such file or directory: '/tmp/tmp_yz6zyfs'

and the program exits with the top-level code having no chance to catch
the ZeroDivisionError and continue execution. (To catch this exception,
the top-level code would need to know to catch FileNotFoundError.)

My view is that if an exception happens within a TemporaryDirectory
context, *and* there is an exception generated as a result of the cleanup
process, the original exception is likely to be more significant, and
should be the exception which is propagated, not the one generated by
the cleanup.

----------------------------------------------------------------------------
System info:

$ python3 --version
Python 3.6.9

$ lsb_release -a
No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 18.04.4 LTS
Release:        18.04
Codename:       bionic

This was fixed in e9b51c0ad81da1da11ae65840ac8b50a8521373c so it's fixed in Python 3.8 and 3.9. Maybe it should have been backported to 3.7.

Python 3.6 only receives security fixes now.

See also bpo-26660 and bpo-35144.

Too late for 3.7 now, closing.