here one possible perl approach for your problem. But regard what Abigail-II mentioned about the I/O-bottleneck.

use strict;
use warnings;

opendir (D,"."); #current working directory
while (my $f = readdir(D)) {
    next unless -T $f; #only textfiles
    print $f,"\n";
    open (F, $f);
    while (<F>) {
        print;
    }
}
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greetings, tos