Ah. Makes more sense. While perl is busy executing display_text(), the GUI doesn't get updated. You need Tk::after or ::repeat for that:

use Tk;
$bottomFrame = MainWindow->new();

my $txt_summary = $bottomFrame->Scrolled( "Text",
                                     -background => 'blue',
                                     -foreground => 'white',
                                     -height     => '1',
                                     -takefocus  => '0',
                                     -width      => '40',
                                     -scrollbars => 'oe',
                                             )->pack(qw(-fill both -ex
+pand 1));

open(FH, "cuentos.txt") || die "no Abrio nada";

sub display_text {
    if(eof(FH)) {
       $bottomFrame->afterCancel($bottomFrame->{RepeatID});
       close (FH);
       $txt_summary -> Insert("\n== FIN ==",'end');
       return;
    } else {
       chomp(my $line = <FH>);
       $txt_summary -> Insert("\n$line",'end');
    }
    $txt_summary->see('end');
}
$bottomFrame->{RepeatID} = $bottomFrame->repeat(500, \&display_text);
MainLoop;
__END__
[download]

But probably you want Tk::fileevent. Note also that "Scrolled" means "attach a scrollbar to it", and not "scroll this widget".

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}