I solved the problem quite simply. First, I read the fscking manual a third time and I noticed that while I was autoflushing the buffer on STDOUT, I wasn't flushing the buffer on the filehandle.

I fixed this by using autoflush on the filehandle:

open (LOGFILE, ">tempLog.$time" ) || die "Cannot open tempLog for writ
+ing: $!\n";
autoflush LOGFILE 1;
print LOGFILE "Socket server started on port $port at ", localtime, "\
+n";
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