Is there a such thing as a Thermostat wire and if so how much does it cost to replace?

Hello, you didn't indicate which engine your Edge is equipped with. Generally speaking, though, I don't see a wiring harness associated with an engine thermostat.. You could have wiring concerns to the cooling fans or with the coolant temperature sensor perhaps, but it's unclear as to what a thermostat harness is. It's always good to ask questions - consult service management at the dealership even if you need to. Alternatively, get a second opinion at a shop near you -- here's a way to find one: www.repairpal.com/repair-shops