Good morning, ALEXBEL,
I would start at the component and see if you have power there. I would warm it up, chock the rear wheels and jack up the front of the vehicle. Support it on some jackstands and go to the wire on the solenoid with a test light. This should be a thin purple or pink wire. Connect the other end to the engine block. Once the test light is in place have an assistant try to start the vehicle and see if you are getting power at the starter solenoid.
If something is changing when it warms up and not allowing power to flow to the solenoid this will tell you. If the light lights up when the key is turned, then it's the starter. Try tapping it with a hammer while an assistant is turning the key and see if it turns over.
How old is the starter?
If the light does not light up, then I would check the Neutral Safety Switch. On your vehicle it is on the top left rear of the transmission. I would try putting it in neutral and see if it starts then. Normally this would cause an issue cold or hot but if the heat of the engine is expanding the contacts because it is in the engine compartment this could cause you to lose power to the starter when hot.
Here is an article that will aid in Neutral Safety Switch diagnosis:
https://www.2carpros.com/articles/how-a-neutral-safety-switch-works
I am also adding a wiring diagram of your starter circuit.
Because of the heat in the engine compartment my thought is it more likely to be a component there than inside the vehicle like the ignition switch itself since it only happens when hot.
I would start there and see if you are either losing power or the heat is causing a mechanical issue in the starter.
Thank you,
Brendon
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Thursday, April 6th, 2023 AT 7:08 AM