Does anyone else have an issue with a hot start causing a misfire in cylinder 3 and if so any ideas on how to fix the problem?

 

If it is a 2000+ this is a known problem. Their is a mopar heat shield or you can wrap the injectors in aluminum foil.

 

Are you running the heat shield? Replaced mine on my '00 XJ when I upgraded to 4 hole injectors. Part# CBXCB060. Jeep dealership actually had it in stock. Cost me $2.20 plus tax. You might pay just a little more. Maybe. I work in an auto parts store and deal with the guys down there. Pretty sure they do the best they can on the price when I buy parts there. Also what are you running for plugs? My '00 had an old heat shield and cheapo Champion Copper Tops. Never had any misfire or heat soak issues. When I replaced the plugs was not about to try another brand.

 

I just replaced my heat shield. Ended up being like $15 and definitely worth it.

 

Any "misery coolant loss?". You have an 0331 head, you might want to search that.

 

I already put the heat shield on and I am still having the problem. I believe I am running champion plugs. I don't have any coolant leaks. The problem is not as consistant in the winter but in the spring and summer when it is warmer if I turn the engine off the turn it back on a few minutes later it will trip the misfire

 

I had the same issue. I used an insulator sleeve/boot designed for spark plugs as per a recommendation I'm pretty sure came from here. Cut it to length, slit it lengthwise, put it around #3, zip tied it and no problem since.

 

Sounds like heat migrating. On a 90 (pretty different issue), my heat shield over the injectors would expand while it sat hot and short some wires to to lower sensors. Took me a year to find that. Sometimes had a 300 mile commute, and left it running all day so it wouldn't do that.

Besides heat soak on the injectors, I need to mention it could be wires. Check/shake that injector harness, verify the grounds are good. (see Cruisers#1 in my sig)

 

If it's happening on cylinder 3, 9.9 times out of 10 it will be heat soak. OP, I don't know what to tell you. I was having the issue on my old heat shield, but it works fine with a new one.