No need to do a total drain for a thermostat installation. However, that may be a GREAT time to freshen the antifreeze. So unless the coolant is relatively new, I'd recommend draining it. And the ONLY way I do it is to remove the lower hose. Forget that stupid petcock. Terrible design and location. Use a 50-50 mix of coolant to distilled water, or buy premixed. Use conventional (green) coolant.
I like stats from Jeep and also the Stant SuperStat. 195 degree only.
Also a good time to review all other cooling system components. Radiator, radiator cap, water pump, fan clutch, serpentine belt, all coolant hoses.