I have a 88xj I've flushed the cooling system out and still have this problem thought it might be over heating but I'll fire it up driving or just sitting give it 15mins it will die. Then after that let it sit for 5 to 10 mind it will fire back up and about 5 mind later dead again just confused

 

Could be an alternator. Lots of possibilities though any other symptoms? What else have you checked?

 

Assuming it doesn't have spark when it's dead you might want to check your cps. I've read it's common to go out, also it can fail when hot. Good luck!

AC voltage CPS (KPS) Sensor test; Small clips on the meter leads really helps.

Unplug the connector at the back of the manifold with wires going down to the bell-housing/cps.
Probe the two wires to the cps with the meter set on AC volts. (a 200 scale on mine).
Crank the engine and note the voltage. (jump it if you battery is low)

Mine somehow works with only .3, my wiring/grounds must be pretty spiffy. .5 seems to be a good mark. One article talked of .5 to .8.