The technique of turning the APU to ON for a bit of time before turning it to START comes from decades ago and has nothing to do with ‘heating’ the APU.
It’s to let the APU start sequencing happen. Mx decades ago said quick application to START could generate the FAULT light we’d often get after the first attempt. “Second start normal.”
The FAULT rate decreased significantly with a pause at the ON position. Over time guys started putting it to ON but not starting it until later, sometimes as long as the entire taxi-in. I’ve done that for decades and haven’t had an APU FAULT during start for years. I’ve seen new FO’s get the FAULT light. I tell them to cycle OFF then ON and leave it for awhile. The next attempt is normal. “Want me to write that up?” “No. It works with patience.”