Does the check engine light come in first try in the morning???
If it is temp related could be a couple of things.
Grounds in the engine passenger side of the block about three important ones. You should be able to locate then very easy. Disconnect and clean with wire brush green scouring pad.
That is the first place to start.
Welcome to the forum make sure to go an put info into your profile page this will help others answer your questions.
See how that works and get back and see what is next.
Sent from underneath my Jeep
89YJ 2.5L TBI, AX-5, NP231 SYE, Tom Woods Shaft, 33" BFG T/As, 4" lift.
AF Jeep Club Tail #184