TMTOWTDI. Here's a non-regex solution:

my $name = 'filename.dqhfhqlkGif';
substr $name, (index $name, '.') + 1, -3, '';
print $name;
[download]

In fact if you change index to rindex, it'll work even if there's more than one period in the name.

dave

Update: Also works with filenames containing newlines.