I want to reduce the power to a aerator pump that is powered by a 12 volt boat battery. The pump draws 3.5 amps. I have tried a 10ohm 10watt resistor (the largest they have) but it gets to hot. Any suggestions would be greatly appreciated.
You cannot reduce power to the motor in using resistor in between. Doing this will cause power dissipation in the form of heat through the resistor and finally the overall power drawn from the battery will remain same. Even if you reduce the voltage, it will draw more current thereby keeping the power consumption same. You can replace the motor with a smaller one to reduce power consumption.
If you reduce the speed, the pump will suck less air / water (whatever it is used for) and thus you'll have to run it for longer time to do the same amount of work and finally the power consumed will be once again the same. This will also be the case with smaller motors.
Finally what I mean to say is whatever amount of work your pump is doing right now @ 3.5A could not be done with introduction of any other circuit / motor with less than 3.5A. The energy requirement is always fixed for a particular work to be done. The only parameter that will vary is time taken to do the work.