One less expensive solution might be a 'bath sheet' / beach towel for the hotter days.
We'll be at around 100 here for the next 3 days with sun loading that is about as intense as it gets (altitude sure does make a difference), and I find that if I get the A/C going for long enough to make the car breathable and have the coolers turned on, that by the time I get into the car, the seats are OK.
When I go for a run, I'll use a Seat Shield cover for the seats so I don't sweat all over the seat. It slides on and off. Might be something you could slide over the seats when you get in to protect against the heat?