What kind of engine/gear?
Every time I ve had a gear running warmer than the other one, especially at slow speed, it turned out to be a raw flow problem. Apparently the gear will run a little warmer before the engine coolant. If exhaust flow if visible, check for a difference between port and stbd. If not, feel the raw water pump cover or check temp with ir gun. In one case, the warmer gear was caused by a pin hole in the fuel cooler on the suction side of the pump (so no leak but air coming in) and another time by debris in the fuel cooler restricting flow. Engine coolant was fine, and gear temp was fine at speed but 20 deg higher at hul speed.