Why does the temperature gauge go into the red when going uphill and return back to normal on flat ground?

I just had the timing belt, water pump and exhaust sensor changed after finding a leak. Now, when the car is going uphill the temperature gauge is going into the red, then dropping quickly when on the flat again which it didn't do before pump was changed. Is it likely to be a problem with the head, even though it passed all compression tests, or with the radiator? The mechanic wants to take the head off.
More likely to be an airlock in the system that can be purged. From cold take the cap off the expansion tank, switch the heater to maximum heat, then start the car and run to temperature until coolant starts gurgling out of the expansion tank, then quickly screw the cap back on. That might fix it.
Answered by Honest John on

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