Since they did replace the heater core, I would suspect the heater valve as most likely since you keep your coolant nice and clean. It is also more likely to go bad in short order compared to the heater core. Unfortunately on those models, they put the valve inside the car rather than out in the engine copartment, but if it is like my 1962 Chrysler in terms of where they mount the valve (upper right side of the firewall above the right kick panel, it might well be accessible but on my cars I almost need to be a contorsionist to get it out. But it is doable. One nice thing about the 60 - 64 models is that the heater core is in the engine compartment (piece of cake!) and changing the heater core in those is preferable to changing the heater valve. But on your car, everything is in the passenger compartment.