2003 Mitsubishi Eclipse overheating

It's probably leaking internally like a head or intake gasket so have a pro pressure check for that.

If you aren't losing coolant then it's probably not the head gasket. But you have just stated the pieces you have replaced. Replace the radiator cap or have it tested at least they lose ability to hold pressure and let stuff like that happen. Then check the mfi and fan relays underhood and see if the red wire leading to mfi and fan relays are getting a signal may not be. Lastly have your fan controller on fan shroud is sending a signal to the fans and whether it is getting a signal from pcm on the blu/org wire. Then lastly check the black wire near left headlight to see if fan controller is got a good ground. Also if you have jumped the fans then the when you put on the a/c they won't work correctly like speeding up. I'd still have the system pressure checked as well though.