climbing; Yup subi,napa, any parts house will have it all. Try changing your rad cap... they can go bad.If that doesn't help then your water pump is another possibility, one you don't want. Usually a water pump leak shows up at the crack of the timing cover but it runs everywhere. Buy a can of brake clean... spray everything that looks wet , clean and dry it, then run your motor. If your lucky you will spot the new leak without going anyplace... if your not then drive it and keep looking. Worry about your heater core later its not the problem . If you don't find & fix the leak ...sooner or later you are going to overheat the motor and you will need head gaskets.