Your alt delete solution is pretty cool. But the electric heater seems a bit wasteful to me.
Seat heaters:
You could try something like this:
Look what I found on AliExpress
High Quality 12V car heated seats /Winter car seat heater car seat heating cushion universal car seat covers-in Automobiles Seat Covers from Automobiles & Motorcycles on Aliexpress.com | Alibaba Group
My car has them built in. Maybe you could use these and dial down your heat.