Threading in Perl is generally not adviced.
Instead, for high performance, you should consider looking into non blocking or event driven programming.
With regular sockets, your process blocks every IO operation, i.e reading from a socket that isn't ready will put your process to sleep until data is available. with non blocking/event driven you poll the sockets and get callbacks when the sockets are ready to be read from or written to, so a single process can multiplex on many sockets, thus providing good scalable performance since you don't need to fork new processes to handle more clients.
There are many good event based frameworks in Perl, e.g POE and AnyEvent POE is a specific event loop with lots of modules and features and AnyEvent is an abstraction layer that lets you use multiple event loops in the same code.
You should also look into libev which is similar to POE but with a lot less overhead.
Writing event driven code is somewhat tricky at first, since you need to be careful with the blocking code you do have, e.g cpu intensive operation, or using libraries which aren't non blocking. because since you have only one process, if it's busy doing something, it can't do anything else - like poll on the sockets and issue callbacks.
So, if you need both non blocking and intensive computations, one way to do it is to create worker forks and use non blocking pipes to communicate between them and your event loop, which is really straight forward with the above libraries.