cherokee93

I have a 93 jeep cherokee. It starts fine. But if I turn it off within approx 10 -15 minutes it won't turn back on. All electrical components (dash lights, radio, door buzzer, fuel pump, etc) work fine, but it won't even turn over. It stays silent as you turn the key. All I have to do to fix it is wait about 10-15 minutes and magically it cranks just like nothing was wrong. If I let it run for a good 10 minutes or more and then turn off it cranks right back up. I've tried shifting to neutral and starting and it doesn't make any difference. I've also put in a battery from another cherokee I have to see if it was a battery problem - that didn't help it start either. This happens pretty consistently. I'm not sure if it is a 'time' issue or if it an 'engine temp' issue but either way I suspect something electrical is preventing it to start and then somehow (time or temp) it decides its ready to start. Any ideas?