It is very hard to flush the coolant system, unless you know where the drain bung for the block is located. The thermostat isn't hard to remove and test, mind you the kettle doesn't get the water hot enough, you would need to stick it in a pot on the stove.
I would try a thorough system bleed, topping up the rear bleed point (heater pipe near the firewall) when cold, you may need to do it a few mornings to get all the air out. Beware, the bleed point is a plastic Philips head, and is very easy to strip.