These symptoms sound just like the heat soak issue that I had with my 2000 XJ before it got totaled. If this is what's going on (and I haven't heard of this happening in a KK before), the under hood temperature rises right after you shut off the engine because the cooling system is not working after the engine stops turning. The temporary increase in temperature under the hood causes the fuel in the injectors & fuel rail to change from a liquid to a gas. This results in sputters and misfires if you start the engine when it's still really hot. See if opening the hood for a few minutes to let the heat out solves your problem. On my XJ I also wrapped the injectors in heat resistant material, which solved about 90% of the problem. Some other XJ owners installed hood vents to keep the under hood temperature under control. Even so, I don't think this is normal for a KK. Are you in a very hot climate or at a high altitude? Does your engine normally run hotter than about 210 degrees (indicating a possible thermostat/cooling issue)?
P.S. There is a lot of info about the "heat soak" issue in http://www.cherokeeforum.com
, including one of my own threads.
2008 Liberty Sport 4x4 AutomaticJeepin By Al 4" Lift Kit
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Full MOPAR skid plates
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AtTheHelm Front Recovery SystemTrailer build thread: viewtopic.php?f=72&t=77997