Line 79 of Heavy.pm is attempting to create a temporary file using tempfile() in File::Temp. If memory serves, tempfile() will not create a directory if it doesn't already exist (that's what tempdir() is for). So File::Temp appears to be complaining here:

unless (-d $parent) {
    ${$options{ErrStr}} = "Parent directory ($parent) is not a directo
+ry";
    return ();
}
[download]

Line 79 of Heavy.pm:

if ($ENV{PAR_CLEARTEMP}) {
   ($fh, $filename) = File::Temp::tempfile(
      DIR    => ($ENV{PAR_TEMP} || File::Spec->tmpdir),
      SUFFIX    => ".$dlext",
      UNLINK    => ($^O ne 'MSWin32'),
    );
}
[download]

Hmm, looks like Heavy.pm is telling File::Temp to create a file in the $ENV{PAR_TEMP} directory which is where your problem lies as $ENV{PAR_TEMP} obviously doesn't exist.

Can't really help you out any more than that as I know little/nothing about PAR and why/how $ENV{PAR_TEMP} is created/used etc...

-- vek --