use Benchmark;
use strict;

my $time_to_die = 15;
my $time_file_1 = "time1.txt";
my $time_file_2 = "time2.txt";
my $current_time = time();    # kept this outside the benchmark

timethese(100000, {
   'Time In File' => \&timeinfile,
   'File Mod Time' => \&filemodtime
});

sub timeinfile {
   if (-e $time_file_1) {
      open (TIME, "$time_file_1") || warn "Can't open Time file: $!";
      my $last_time = <TIME> || warn "Unable to get timestamp from file: $!";
      close TIME;

      if ($time_to_die >= ($current_time - $last_time)) {
         open (TIME, ">$time_file_1");
         print TIME $current_time || warn "Unable to write timestamp to file: $!";
         close TIME;
      }
      else {
         unlink($time_file_1) or warn "Can't unlink file: $!";
      }
   }
   else {
      open (TIME, ">$time_file_1");
      print TIME $current_time;
      close TIME;
   }
}

sub filemodtime {
   if(-e $time_file_2) {
      my $last_time = (stat(_))[9];

      if($time_to_die >= ($current_time - $last_time)) {
         open (TIME, ">$time_file_2");
         close TIME;
      }
      else {
         unlink($time_file_2) or warn "Can't unlink file: $!";
      }
   }
  else {
    open (TIME, ">$time_file_2");
    close TIME;
  }
}

Benchmark: timing 100000 iterations of File Mod Time, Time In File...
File Mod Time: 11 wallclock secs ( 6.97 usr +  3.21 sys = 10.18 CPU)
Time In File: 48 wallclock secs (21.26 usr + 25.77 sys = 47.03 CPU)