Engine temp/heater issue

I have a 1998 Chrysler Cirrus. The heater alternately blows cold air and hot air, and the engine temp soars quickly then drops just as fast. I have replaced a suspect radiator cap, topped off the overflow tank, and replaced the thermostat, nothing seems to have helped much. Could it be an air bubble that ingressed either through the overflow or the faulty cap? What should I try next?