Cps failure would not let the Jeep turn over or fuel pump run . I'm currently have a similar problem . 
My XJ  starts ,runs and drives at first but once it gets to normal operating Temperature it dies and although it we starts it won't run until its cooled down again . 
So far I've replaced the cps , lambda, ,temp sender, tps been through all the earth's and cleared the ECU connections no luck so far .