Temperature spikes

I put in a new water pump(not reman/rebuilt. Purged air from cooling system and it has been fine since until now. I only have second hand info from my son who is 800 miles away with the car for the summer in Alabama heat which has been running over 100 degrees daily for a week or more. Yesterday he called when a warning came up on the info system that it was getting too hot. He was on his way home so I had him stop & get a gallon of coolant before he got home. This morning the "bottle" had fluid in it but I had him uncork the filler tube and add coolant there until it was back filling the "bottle" and overflowing the tube. He took it on a short drive and watched the gauge. It spiked a couple of times to hot particularly at traffic lights, but came back down into the normal range each time. Turning on the heat & fan helps too(fun at 100 degrees. Worse with AC on. Should I suspect the thermostat? Cooling fans and or relays?
I need to advise him before he looks for someone to fix it and it needs to be fixed long before he makes the trip back here.