It depends on what you asked the dealer to do and what the dealer said was the problem. Your case would be best if you went to the dealer and asked them to look over the cooling system and repair what was necessary. If you did the diagnosis and asked them to perform the specific repair you requested, they are responsible only for doing the repair competently. If you can prove that they did not do the repair competently, you might have a case. Like if they removed the heater hose and did not reinstall the clamp, or something. But if your heater control valve broke due to age, that is your problem. You need some sort of negligence on their part, and I don't see any from what you wrote. That does not mean that there is not any; there could be more facts that are important.

Philip Bradley