I would advise to keep the gun sealed well. Put it in the truck somewhere far away from you.
Your car is probably quite moist during winter, you bring water (snow) in on your boots and then use the heater to melt it.
On top of that your breath brings in moisture. The worst of all is wet or damp clothes, they do dry very quickly in the car but where does the water go... If your windows are closed, pretty much nowhere.
The heater is not a problem as it is required to keep your breath from fogging the windscreen. With good and timed air flow, you can use it to your great advantange.
I do the followings to keep my tools from rusting:
Gun:
Keep gun in a bag, it will insulate and smooth out temperature swings, this alone might do it. On top of that it reduces the AIR FLOW near the rifle because every cubic inch of air holds some water and your cold rifle collects it like it was paid to do it. Add silica bags inside your gun bag.
Car:
Kick you feet together to drop any excessive snow before taking them inside the vehicle. Remove puddles.
If you park during the day, roll windows open to let the dry air replace the moist air, just an inch wide helps a lot. I usually choose to keep the just the rear windows slightly open as they are not electric. But do close them for night if it is not very cold, as your windows freeze during the night = moisture enters back inside.
Air the car by having all doors open if you are waiting for someone.
If you use the heater, realize that the water has nowhere to go, unless you open the windows to let the moist air out, it will just suck mainly into your cushions, ready to fog your car when the temperatures drop enough outside the car.
Edit:
If your chamber is fine, then that coloring is indeed just the suppressor's fault. I have never noticed the "steam-carbon pressure washed" cartridges to be any more inaccurate than shiny ones.