'02 Jeep Liberty won't start when hot

Here's what I did to fix it. My '02 Liberty won't start when hot. All dash lights work, everything seems ok but the engine won't crank until it cools down. I replaced the starter (no fix), I replaced the ignition switch actuator (no fix), I tested everything and couldn't find the problem. So I spent $10 for a push button start button. I ran a hot wire from the fuse box to the start button then a wire from the start button to the small starter wire. (Problem solved). Now when the car is warm and won't start I turn the key on and push the button.