Hi Mom...if you're hoping to hide speakers (or a speaker) in the old heater, you'll need a bluetooth receiver/amplifier. This will pair with your phone (whatever type it is) and let you do this. I haven't bought one of these yet, but something like this might work for you and it does have volume control:
https://www.mouser.com/ProductDetail/DFRobot/DFR0803?qs=DRkmTr78QATeH9Juc%2Fy45g%3D%3D I plan to get one of these if for no other reason than experimentation.
As for rewiring, I'm probably not the average bear but I'd be inclined to buy the wire, connections, etc and build the harness myself.