Re: 2003 3.3 mercury gets hot but does not overheat.
Is there water coming out of the tell tale hole? This is the little stream of water that should be spraying out the back of the motor when it's running. If not, then it's most likely the impeller in the water pump or a blockage in the input to the water pump. That are a couple of web sites (boats.net) that will have exploded parts views of of your motor that will show where these things are. If both the impeller and the intake are fine, there is a small diameter tube, usually made of copper, that carries the water up from the water pump to the power head. There are seals at both ends of this tube that should also be checked. The water pump maybe working fine, it just maybe that the water isn't getting to the motor. It doesn't appear that the 3.3 hp mercury has a thermostat so that shouldn't be the problem.
Good Luck