Does it also overheat if you are sitting at a stop light or going through a drive-through? Make sure it has the proper coolant mixture at the correct level. Are the fans working properly? The check engine light may be able to indicate if there is a fault in the cooling system, if it's on. It would advise you to see a mechanic that is familiar with Jaguars and specializes in diagnostics. You don't want to overheat your engine and cause further damage.
Get car to a shop asap. Overheating can quickly damage engine. Most likely cause of overheat on hills would be the fan clutch, electric cooling fan, or restricted radiator.
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