That's what lowpass filters are for.
Well, yeah - it's naturally constrained. When I jack the temp target on the A/C here, it take 30-45 seconds to turn everything off.
Tim used to be a lot of fun and put up with much. FWIW rbj showed up on Reddit and lasted a couple days.
You're just doing trust falls with slew rate limiting. :) There's probably a PhD paper somewhere with a madman low-pass filtering the output of a bangbang with a lowpass.
Kinda like... the .047 uf cap in the tone circuit on a Telecaster :) It's there to limit damage.