I don't know if the heater core will flow with the tstat closed. That's a good question. Hopefully someone else can chime in.
However, if the top radiator hose is getting hot, then that's not the problem. Does it open inward toward the motor or outward toward the radiator?
However, if the top radiator hose is getting hot, then that's not the problem. Does it open inward toward the motor or outward toward the radiator?