I have a Payne heat pump that is not cooling down ...

There are multipule factors.1)clear drainline,2) clean filter, 3) clean coil, 4) if refigerant is low there is a leak that needs to be repaired - "freon" is like water in a cars radiator, if it is low you have a leak. Leaks get worse not better.

if you already know the unit is low on freon than you already know the problem, it has  nothing to do with the thermostat. the unit operates at certain pressures and that's were freon comes in to play, if you short of freon unit will not work right if you have to much freon the unit will not work right, fix the leak and charge the unit if your not a A/C tech please call one in to do the job. good luck