The heater core shouldn't be too hard to replace but I can't say on your truck, but I don't think that alone would be enough to cause a serious overheating problem. Theoretically, it does help lower the temp of the coolant. I could be wrong, but I don't believe the heater core is your immediate problem.
Like I said, the first thing I would do is put a "known good" temp guage to see if your readings are correct. If your guage is faulty, you can replace the complete heating and cooling system and you could have the same problem.
Good point Rnuts on the plastic circulator.
