You should check to make sure that the electric fan is working.
Check the 92 Eclipse for vacuum leaks. Check to see that all of the spark plugs are firing properly. Check to see that the fuel injectors are working. Either of these could cause the rough start and rough running.
AC/Delco
Check firing order Two of the plug wires are crossed.
Engine miss/running rough. Engine back firing / poping
Check spark plugs and wires Do a compression test
At 35mph it runs rough. Also when idling it will quit running, sometimes. Does that sound like I need new spark plugs? How many miles are new plugs & wires good for?
The injectors or spark plugs might be firing wrong. You should get it checked out as soon as possible.
if the car is running rough or if plugs are in poor condition
Rough Engine Performance AFTER Changing Distributor Cap and RotorThe only thing I can think of is that in the process of the changeover, the wires between the newly installed rotor and the spark plugs were not reconnected to the proper "towers."As a result, the spark plugs are not firing in the proper order thus causing the rough running. Since the engine will run, I also suspect that possibly only one or two plug wires are improperly connected.
check spark plug gap and firing order-also check to make sure plugs are tight and wires connected
When the idle goes rough, you must idle the plugs. Else the car plugs roughly.
If it starts very rough but then clears out expect either fouling of spark plugs or a mixture problem that clears up when O2 feedback becomes available. As far as the gage showing overheating... does it show this immediately after a cold start? Have you considered actually taking its temperature with a suitable tool?