From my conversations with her, let me explain what I understand. The temperature question isn't about overheating, its an observation that I've made talking to her that once the car is warmed up, it is difficult to restart. When it has cooled down it starts although I'm not sure if it starts normally or just easier and if this is consistent. This makes me question whether it's a thermal issue with an electronics module (PCM,RCM, a sensor, or??). I am also wondering if it could be fuel starvation, It would be helpful to know what the fuel pressure is under normal and non starting conditions. She did have the fuel filter replaced by a local mechanic in Fl a few weeks prior to leaving and had no issues until the trip. I believe she said it was an STP filter. She said that once the car started it ran ok. It has no issues cranking, just starting. The check engine light is on again. Unfortunately, she said that in California, she cannot get the codes read at the local auto part store (is that a state law?).

At this point I think that she needs to find someone local that can look at the problem and diagnose what is going on. First check what error code is set and fix that, second check fuel pressure when it runs ok and when it won't start, third check electrical (ignition, spark,....)
Some other thoughts, Could it be an issue with the SKREEM module? or possibly an aftermarket alarm, is there an aftermarket alarm installed?