A more aggressive approach is also possible, besides yours and tachyon's. The unlink call can take a list, so lets try unlinking all the unwanted files in each directory we see on the way down the tree.

#!/usr/bin/perl

use strict;
use warnings;
use File::Find;

our @ext = qw(.tmp .bak .$$$ .chk .old .gid
         .fts .ftg .log .dmp .--- .prv .temp);

sub wanted {
    my $dir = $_;
    -d && unlink map {glob "$dir/*$_"} @ext;
}
find (\&wanted, $dir);
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Since find runs wanted() before entering a directory, this approach reduces the number of files find() must look at.