Try this:

Ensure coolant level is correct.

Proceed to go uphill til you notice the temp is higher than normal.
Check the engine bay for any signs of coolant (try not check this as fast as you can, before it dries up)
Sometimes minor leaks, and will worsen when engine is under load (eg; going up hill in your case.

I faced this issue previously, no signs of leak until engine under load uphill, then there is coolant squirting from one side of the rad.