2007 Jeep Commander Misfiring if allowed to idle or while driving at slow speed in traffic.

Hello all! My name is Michael and I have a 2007 Jeep Commander which I love. There has been an issue with it since I bought it (used)m and I've had it to several (more than 4) mechanics and even a Jeep dealership and no one has been able to figure out what is causing the issue. I'm hoping someone here will have some idea of what it is.
First I should state that my Jeep Commander has a rebuilt engine in it. I didn't know about this until I had a new transmission put in, and the mechanic told me the engine block is stamped "Rebuilt by Chrysler".
Anyway, here's the issue: In the summer (ONLY), when I am driving and stop at a trafficlight or stop sign or whatever, if I stay stopped for more than a minute or so the engine starts to misfire. Then it continues to misfire releatedly once I start going again and will barely move forward (constantly misfiring) until I creep up to a speed of around 35 mph or higher. Then the misfiring becomes intermittent, and then the misfiring stops completely, until the next stop.
If I turn the engine off as soon as I stop at a traffic light or whatever, then back on once I can go again, it doesn't have the misfiring issue.
So, it seems it only happens when it's hot or warm outside, and only when it's idling or if I'm in a traffic jam and moving very slowly. The check engine light comes on, and there are different random codes along with the misfire codes (the misfire codes are not always the same cylinders).
Mechanics have checked the fuel injectors, cylinders, idling temperature, everything they can think of and they have no idea what it is.
Bottom line: In the cooler months, when the vehicle is moving at a normal speed and not idling for long, it runs fine. In the warmer/hot months if I turn the engine off when I stop and turn it back on when I can go, it runs fine. If I let it idle or if I have to drive very slowly for traffic it will start misfiring. The vehicle struggles to go forward after the misfiring starts, and keeps misfiring until I get to a speed of 35 mph or more then it stops misfiring. The check engine light stays on for a few days, and as long as I don't let it happen again, the check engine light goes out after a few days.
Anyone had this issue before or have any ideas? It seems like it might have to do with the internal temperature of the engine, and possibly the ECU getting hot when the vehicle is idling, but the mechanics I've taken it to said that's not it (but they also have no idea what is causing it.)
Help? Input? Thanks all!