Hi Lars
Well that's too cold for my bones!
Just try and keep the temperature constant between your lights and darks. A couple degrees difference is okay.
Don't forget also that if you do get a mirrorless, to get the best out of it, you should look to modifying it to increase Ha transmission. That could increase the budget a fair bit.
The ASI6200MM is an amazing camera! To be honest if I was buying a camera solely for astro work, then that is what I'd be using.
As for dust, have you tried these? I've used them on my cameras over the years with good success
https://photosol.com/products/sensor-swab-ultra/