The thermostat is a self-contained unit.

I had a problem on an Aries K with a bright shiny new thermostat. Still badly overheated on waiting for the 1st opening of the t-stat. Turns out there was steam in the housing on the hot side of the t-stat, which could not heat the t-stat as well as the cold water on the radiator side could cool it.

Check to see whether the top radiator hose is warm-to-hot while the reservoir is getting filled. If the hose stays cold, the t-stat is not opening. If that is the case, you might be having a steam bubble behind the t-stat. Drilling a small hole (maybe 3/32") in the main flat part of the t-stat, and installing it so that that hole is as high as possible will probably be a fix.

As soon as the upper hose gets hoat, fell the front surface of the radiator to see whether there are hot and cold parts. If there is a lot of difference, you might have some blocked tubes.

Make sure the bottom hose is not collapsing.

Some arrangements really rely on flow through the heater core to create the circulation that brings hot water to the thermostat when it has not yet opened. Without that flow, the water around the combustion chambers and cylinders can overheat due to the lack of circulation. Feeling the temperature of the heater hoses while the engine is first warming up can confirm whether you have sufficient flow there.

I can answer on that question,by coolant owerflowing is shown that you have problem whit cylinders cover gasket .No need to check the termostat this maintenens is full including engine overhaul procedure and replaicing
cylinders gasket.