Its worth a shot. I dont see any alternative if you say the you have no other options.
Take it out of the soil, and wrap the roots in a wet paper towel. Dispose of the current soil, and replace it with new stuff. I microwaved all of my dirt to kill anything living in it. I zapped it all for about 2 minutes, or until it had been steaming for about 30 seconds. I havent had an issue, and my soil came from my garage- where its been since spring.
Once you have the new soil ready to go, turn your attention to the plant. Do whatever nessecary to get every last mite off of the actual plant. Replant.
I would find another place to keep it though- as your room still probably has a large infestation of mites, and youll just end up with the same problem. Id at least wait a few days before putting it back in your room if possible (although 30deg temps in the garage arent helping things either). I think you noticed an improvement in the garage because the cold could be killing your mites. Too bad its killing your plant too.
Best 'o luck, man.