Why would the engine temperature increase

I don't think your engine temperature is varying that much so I would suspect that the voltage being supplied to the gauge is not consistent. Check the alternator belt and the voltage at the battery with the engine running to see if it's steady.

Check coolant level and check for air in the cooling system. If your coolant level is low you might have a condition where the coolant is sloshing around in the block. When this happens the coolant sensor will pick up the temp of steam/coolant mix and of straight coolant. If the sensor is steady at first then becomes erratic as it warms up this would identify your problem.