Put the new thermostat in, with the element on the engine side and the gasket on the radiator side. Reattach the housing and put the plug back into the radiator. Top off the system with a mixture of water and non-phosphorous antifreeze. Check back on it in a couple days to see whether it needs a bit more water due to air being purged. Like we said.
Thermostats are a fairly simple device, but even they can fail.
This procedure will correct any faults that were caused by a thermostat of the wrong temperature range, one that's stuck open or closed, one that doesn't move as far as it should, or one that responds at the wrong temperature. And, since it's cheap and easy, it should be near the top of cooling system diagnostics. In our case, we found the thermostat in the car was rated for 87 degrees C, much too warm. So the swap did in fact result in cooler running temperatures. Nothing perks you up like 120 volts to the nads.