Why would a Geo just shut down going down the road but then after it sits start for awhile?

possible overheating of fuel pump, or fuel pump relay (if equipped). Or possible overheating of other component. Sometimes clogged fuel filter can cause electric fuel pumps to overheat. If you do change the pump MAKE SURE you also replace the filter. also the ignition module (if equipped) sometimes overheats and causes warm start problems. If you are going to troubleshoot this problem yourself, dont skimp, buy the repair manual, mine shows how to test all the sensors, so you dont replace everything you suspect MIGHT be bad.