Wrong. Just the wasted energy turns to heat. Wasted by means of mechanical/electric friction. The usefully used (to put it this way) get's transformed in kinetic energy (platter rotation)(most), other electrical energy (transformers) and more.
Talk to anyone who has ever run a datacenter. The heat output of a machine is exactly equal to the amount of energy consumed. Maybe a watt or two leaves the room as electrical energy on a network cable, as sound energy, or as EM radiation.
Where else does the energy go?
Look at this as a freshmen year physics thermodynamics problem. Your system of interest is the computer case. It has 500 Watts coming in. It has 0.5 watts leaving as EM radiation, 0.5 watts leaving as sound (i.e., vibrations in the air), and 1 Watt leaving on wires connected to it. The other 498 Watts are necessarily heat.
Eventually all the kinetic energy in the spinning platters is converted to heat. It is converted continuously to heat by the process of friction between moving parts, and by the time the platters stop moving, all of it that was kinetic is now thermal.