Just yesterday on our 85 degree day here in Michigan I took the doors off the XJ and went for a cruise. When I got into town, I shut the jeep off, went for a short walk, and when I got back and started the jeep, it idled fine for a second, then bogged down and hit about 400 RPM's. Put her into gear, chugged a bit, lurched me backward out of my parking space, but once I got moving on a main road and took it past about 1.5k RPMS it leveled out and would idle just fine. I'm thinking it's the injectors getting really hot from the Exhaust Manifold. Any thoughts, or solutions besides a manifold wrap?

 

i think you're on to it with heat soak, but could also be a sensor going out.