Yes, this would take a lot of memory if you read in a large file to a string first.
To force download of a large file, just print the file as you read it in like this:

if(-e $file) {
    if(open(SESAME, "< $file")) {
        print "Content-Disposition: attachment; filename=$file\n";
        print "Content-Type: application/octet-stream\n";
        print "Content-Length: " . (-s $file) . "\n\n";
        while(<SESAME>) {
            print $_;
        }
        close(SESAME);
    }
    else {
        print "Content-Type: text/html\n\nError: Could not read from f
+ile\n";
    }
}
else {
    print "Content-Type: text/html\n\nError: invalid filename\n";
}
[download]