merlyn has a nifty routine for that, which I shamelessly stole for Simple HTTP in under 100 lines :

$SIG{__WARN__} = sub { warn __stamp(shift) };
$SIG{__DIE__} = sub { die __stamp(shift) };

# This sub Copyright (c) 1996,97,98,99,2000,01 by Randal L. Schwartz
sub __stamp {
  my ($message) = @_;
  my $stamp = sprintf "[$$] [%02d@%02d:%02d:%02d] ", localtime[3,2,1,0
+];
  $message =~ s/^/$stamp/gm;
  $message;
}
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After that, all your output to STDERR (warnings, dies) will be prefixed with the (time)stamp.