If your motor is drawing too many amps for your ESC and it's shutting down or overheating or it wants to much from low C batteries and you are cogging as a result, gearing down generally won't help enough, it's a hardware issue that is best fixed with different hardware.

If your question was meant to be phrased more along the line of using amps as a synonym for temperature then the answer is yes and no. A smaller pinion will make your motor run cooler until you go so small that you're driving at full throttle all the time and then the heat will actually increase.