rough idle When hot starting
 

I have a 96 xj and recently when I drive it and let it sit for 10-15 min and then restart it, it starts but idles very low and the whole car shakes. I'll step on the gas but I get no response and it won't stop and eventually it will jump up in Rpms and then idle normal or it will shut off and I will have to let it cool down for a while. When its shaking I look at the oil pressure and it's very low at about 10 (runs at like 50). I have looked on the forums but haven't found anything. Can anyone enlighten me?

Very common and well known issue. The problem is called "Heat Soak", where the head from the exhaust manifold boils the fuel inside the fuel injectors while the vehicle is sitting with no air flow to cool it off.

When you first start it, it's not burning enough fuel, so it misfires.

Very annoying problem. Finding a way to reduce under-hood temps or shield the injectors are the best solutions.

You could also have one or more injectors that leak down when the engine is shut off.

Get a can of BG 44K and put it in your gas tank. That will un-gunk most injectors.

IIRC, 96 didn't have a heat soak issue with their injectors and it is winter time now.

Mine still has the heat soak problem despite out door temperature.. it's not as bad when it's cold, but it still happens.

Also, if it were injectors leaking down, it would happen every time you started it, not just when it's hot.

I've heard that if oil pressure is dropping that much at idle it's a bad oil pump. That said, if the cel is on get that checked ASAP, also the o2 sensors could have some play in this..

96s didn't have the heat-soak problem like your year did.

I also associate hot-starts with the fact that the engine is still warm from the previous shut-down and there is raw gas in the manifold. On a cold start, like a following morning, the gas has evaporated already.

Thanks my buddy works at a shop and I'll see what he can do for me I just wanted to get pointed in the right direction. Thanks!

Fuel pressure test. See if it holds pressure after shutdown.