'Filename extensions' are a proper subset of 'suffixes'.
https://en.wikipedia.org/wiki/Filename_extension
Dan 'solutions' indicates that he thinks that the two sets are or should be the same, which they are not. The only thing that is DOS/Windows specific is its more special treatment of '.'.  That said, I can see how a Windows user might be confused by the following awkward sentence.

    If 'suffix' is specified, the file name will end with that suffix,
    otherwise there will be no suffix.

as 'no suffix' is easily read as 'no extension. The manual, but not the docstring, addresses the possible confusion by adding

  mkstemp() does not put a dot between the file name and the suffix;
  if you need one, put it at the beginning of suffix.

I think the prefix sentence is also a bit awkward.

    If 'prefix' is specified, the file name will begin with that prefix,
    otherwise a default prefix is used.

I think both parameters should be explained in both docstring and doc with one shorter and clearer entry.

"The file name will begin with *prefix* (default 'tmp') and end with *suffix* (default ''). The is no automatic addition of a period ('.') before the suffix."