Well, starting a car for half an hour every few weeks is just about the worst thing you can do for it. If it were mine, I'd remove the battery and bring it to an indoor garage to keep on a battery maintainer (preferably something like the Solar Prologix that won't just constantly float charge it, but will run it through a maintenance cycle of small charges/discharges.) Yes, I know the "cloud cars" have the battery in the wheel well and the wheel has to come off- but its better than the damage caused by idling for 10 minutes every few weeks.
The best thing for the car would be if every 3-4 weeks it could actually get DRIVEN and brought up to full operating temperature and held there for a while. If you can't do that, don't even start it at all. Turn the HVAC off to close all the exterior air inlets before shutting it down, and try to do what you can to keep rodents out from under the hood as well. Air the tires up a little over-pressure, or consider putting it on jackstands to keep from flat-spotting the tires.