Q: Would a blown coolant hose, at heater core, cause loss of power?

Yes, severe overheating will cause loss of engine power and also has a high potential to damage the engine as the pistons scuff the cylinder walls and the exhaust valves stick in the valve guides. If the overheating is severe and prolonged, loss of cylinder compression can occur. To get some idea of the present condition of the engine you can do a compression test on each cylinder and see how the results compare to factory specifications. With regard to the cooling system leak, if you already know the source of the leak, that should be easy to repair. If you do not know the source and/or you want the entire cooling system pressure tested for leaks simply request a cooling system leak diagnostic. Please note that the engine cooling thermostat can be damaged by the high heat that occurs during overheating and it should be replaced. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.