[LazyPup]

If we were examining an internal combustion engine we could say that heat is a product of work, and if the motor is oversized it will basically play with the load, therefore it would run cooler than a motor running at full rated load, however such is not the case in an electric motor.

In an electric motor energy is consumed by making electro-magnetic fields in the motor windings. Regardless of what size of load we have the size of the windings remain the same, thus the amount of magnetic flux produced remains nearly constant. If the magnetic flux is induced into an armature it is then dissipated in the form of mechanical motion by the rotation of the motor however the mechanical energy is still in the motor unless we attach a load to which the motor can transfer the energy. When the amount of electrical energy being drawn into the motor is in equilibrium with the amount of mechanical energy being drawn out of the motor the only heat generated is the heat of bearing friction and a slight loss to hysterisys currents or electrical eddy currents in the motor windings.

Now let us consider what happens if we oversize a motor.

746watts of electrical energy equal 1 Horsepower of mechanical energy.

Let us use your example of a 3/4HP motor in the place of a 1/2HP motor.

If 746watts = 1HP we can then say 3/4HP = 746 x .75 = 560watts and 1/2HP = 746watts x .50 = 373watts.

The 3/4HP motor windings would now draw 560watts of energy which they convert to magnectic flux. The load is only equal to 373watts of energy so we have a remaining balance of 560w - 373w = 187watts of energy

Understanding that energy can neither be created nor destroyed it stands that the excess energy must go somewhere. In this case the 187watts of excess energy entering the motor cannot be consumed by the load so it has no alternative but to dissipate in the form of heat within the motor windings. To give you a rough estimate of how much heat that is, consider that a MR.Coffee coffee maker has a 175watt hotplate to make it function so in a sense we could say that by replacing a 1/2HP motor with a 3/4HP motor we are expecting the motor to operate with a 187 heating element buried in the windings.