This is working on my pc.

use strict;
use warnings;

my($NEXT_TIME,$FILE_NUMBER,$LOG_FILE);

$NEXT_TIME=time;
$FILE_NUMBER=0;

while(1){
    if ( time > $NEXT_TIME )
    {
          print "Change file next=$NEXT_TIME\n";
          thread_log();
    }
}

sub thread_log
{
#closing the handler to the current file
if ( -e "log$FILE_NUMBER.log" )
{
  close($LOG_FILE);
}

$FILE_NUMBER += 1;
open( $LOG_FILE, '>', "log$FILE_NUMBER.log" ) 
    or die "Unable to open logfile:$!\n";

$NEXT_TIME = $NEXT_TIME + 10;
}
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It seems the problem is in other place. How you invoke threads?