Hmmmm.. Idk about man.. That almost sounds like maybe a short or something. Idk mine just would turn over. And acted like it had no fiel or spark. And the Fuel gauge wouldn't show. If I let it sit over night and try it the next morning it would start fine.. I went ahead and started at the fuel pump. Installed a Bosch fuel pump. Solved some of my phantom issues I had but would still do the same hot weather deal.. I finally got a "no bus" message on the odometer. After researching a million threads I found it could either be a bad plug/ground connection or the crankshaft position sensor. So I have literally looked at every connection, cleaned them. Still did it. I ordered a Mopar CPS sensor.. Hopefully this week when I get it it'll take care of the issues.. On yours I would start at disconnecting the radio. Then making sure no lights are on, no doors open, etc.. (No power being used) Then disconnect the positive cable from the battery. Rub the cable connections on the positive battery terminal.if u see some sparks it may be a short that bleeds your battery down. Combined with high temps can drain a battery. Much like the cold. If there is a short short then track it down. Maybe start there man, I'm an avid DIY guy but no mechanic. So I hope that helps your jeep.