$SIG{ALRM} = \&Done;
alarm $timeout;             # Set your timeout here, in secs

while (<INPUT>) {
   print OUTPUT $_;         # Do whatever
}

alarm 0;                    # So as not to trip ALRM after we're done with INPUT
close(OUTPUT);              # Likewise, in case we got an EOF in INPUT before $timeout
close(INPUT);

sub Done {
   close(OUTPUT);           # Do your cleanup and optionally exit
   close(INPUT);
   exit 0;
}