open (FLAG, '<', "flagfile") or die "cannot open flag $!";
flock FLAG, LOCK_EX or die "cannot lock file! $!"; #mode 2

# you have an exclusive lock to FLAG here..
# by cooperation convention, I that means I have exclusive
# access to both the LOG file and the TEMP file
# other processes don't update or use either 

open (LOG, '<', $file) or die "cannot open $file $!";
open (TEMP, '>', "tempName") or die "cannot open tempName $!";

# there will only be one "tempfile" at a time, so the name
# doesn't matter much. Add your program name into it so that it is
# unique amongst other processes and I think that's all you need
# i.e. no rand() required.

while (<LOG>)
{
   # process each line in LOG
   print TEMP "whatever";
}

close LOG;      # this would release the lock
                # but we are using a different lock 
                # for IPC coordination.
unlink $file;   # I think necessary for the rename of the temp
                # file to the log file's name.
                
close TEMP;
rename "tempName", "$file"; # "LOG" replaced with 
                            # the edited version
close FLAG;  #releases lock.