Celica still overheating after all new parts
My 2000 Toyota Celica Gt-S has had a new radiator, radiator fans, thermostat, water pump and battery replacement. All the parts were purchased and installed new. The car still is overheating. I noticed that when the car was fin with all parts installed, the heat no longer was working. The vents only blow out cold air no matter the set position, temperature doesnt change at all. There is no warm air or feeling of any hot air pushing through the ventscat any time. Just stays the same. The cars temperature gauge also is acting funny and wants to rest at one more marked level above normal operating temperature. It will drop back down to the normal range and go back and forth. eventually the guage will read Hot and I will go to pull over and by the time I get stopped and just about to turn the ignition off, the gauge drops back down within its normal range. So I don’t know if the car is actually over heating, or if the car is over heating but the guage isnt reading properly for whatever the reason? My main questions are could the new parts have been installed incorrectly?