It sounds like the coolant is not circulating. It sounds like you changed the T-stat as a “fix” when perhaps the problem was elsewhere in the system.
Since the water pump and T-stat have been changed, the possibilities that come to mind are a clogged radiator, a collapsed inner liner in a hose, an sir pocket, and (since you mentioned cold weather) perhaps an ice blockage still existing from water resting somewhere from the prior work (I’ve never heard of this, but it cam eto mind anyway).
I’d suggest starting by flow checking the radiator and the engine with hoses. Perhaps I’d test the hoses in hot water to see of the inner liner is collapsing.
Another test you’ll want to do, sincethe engine has been repeatedly overheated, is a compression leakdown test. There’s a very good chance that you’ve blown a headgasket. That may be your single biggest problem.