For a quick solution, without having to rely on (the far superior) modules, I've often used this code (which could certainly be improved). Just pass the starting directory on the command line.

#!/usr/bin/perl

use strict;
use warnings;

open my $LOG, '>', "$0.log";

my $startdir = $ARGV[0] || '.';
push my @dirs, $startdir;
while (my $dir = pop @dirs) {
    opendir DIR, $dir; 
    my @files = grep !/^\.\.?$/, readdir DIR;
    closedir DIR;
    foreach my $file (@files) {
        my $fullname = "$dir/$file";
        $fullname = $file if ( $dir eq "/" );
        if ( -d $fullname ) {
            push @dirs, $fullname;
            next;
        }
        if ( -f $fullname ) {
            if ( $file =~ /\.dat$/i ) {
                print $LOG $fullname . "\n";
            }
        }
    }
}
close $LOG;
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You will of course have to add the logic for checking the tile modification time. A shortcut for that is:

my $mtime = stat($file)[9];
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Unless, of course you need the other values that stat returns.