We are upgrading to a wireless thermostat but the wires in the wall are extremely short. Is there an easy fix?

Pigtail new wires using wire nuts or solder extensions. You can buy a short piece of stat wire at Home Depot. If you need only 4" or so, they will probably give it to you.

Make SURE you get wire with the same colors. Get enough wire to push the connectors back down into the hole. There won't be enough room in the state sub-base for even the smallest connectors. Get a foot of wire so you have something to work with, after you make the connections you can cut off the excess. Stagger the connections so you don't have a big bundle in one spot.

Just for the record, all connections must be in the outlet box.

You cannot connect splices outside of a box.

Just for the record, all connections must be in the outlet box.

You cannot connect splices outside of a box.

Just for the record, that does not apply to low voltage wiring... speaker, telephone, intercom, doorbell and of course thermostat. Keeping in mind that there are line voltage thermostats, it's pretty unlikely that the wireless one the OP mentioned is line voltage.