The thermostat does not have to be changed when changing the radiator.
However if you're removing the hoses and replacing the radiator then it may be a good idea to replace the thermostat as well.
And if the radiator hoses are 10 years old or older it would be good to replace the radiator hoses at the same time you're replacing the radiator.
You can run a car or drive a car without a thermostat.
However if you run the car or drive the car without the thermostat then the engine won' reach it's operating temperature and the heater will usually not blow hot air.
If you drive without a thermostat, your engine will never reach its optimal operating temperature and your heater may blow cold air.
It happens because driving without a thermostat tricks your engine into thinking it is cold outside, causing it to adjust the gas mixing valve and push more fuel to the engine.
The thermostat opens and closes to keep the engine from overheating and to keep the engine at the proper operating temperature.
So it's best to have a thermostat in the engine although running the engine for a short amount of time without a thermostat if needed is okay.
Your car thermostat is an important part of your cooling system.
As the coolant gets hotter, the thermostat opens, allowing coolant to flow through to the radiator to be cooled.
The thermostat then opens and closes to keep the engine within a certain temperature range.
A engine thermostat is really cheap and worth the money to replace as it keeps your engine working properly and keeps your heater working as well.