Tips on Insulation for Hibernating Ants

[OBlock123]

I live in New York and have a big colony on Monomorium Min ants (2-3k workers) and I've been gearing them up for winter. I've been keeping them in a mini fridge on the lowest temp for the past few weeks; started by just putting them in at night but now am getting them used to a few days at a time. This is my first time using this mini fridge so I just bought some refrigerator thermometers and the readings are a little startling.

Apparently on the lowest temp setting, the temp inside the fridge is 36-41 F (2-5 degrees C). So far the ants have been able to cope with this and I haven't seen a significant drop in numbers during the day time when they are taken out of the fridge. However I am fearful of the prolonged exposure to this kind of cold. Their main nest is in an AC outworld that is filled with dirt (Ive disconnected most of their other connected outworlds except for the AC Tower they use as a bathroom/graveyard), and I know the main hub of the colony is directly at the bottom of the outworld, so many workers would be hibernating directly on the plastic floor as opposed to dirt.

Any suggestions for good ways to provide insulation to the colony? Just an added layer of protection that will help the inside of the enclosure stay a few degrees warmer. The ants were caught in upstate NY, and have shown to be incredibly resilient, so I dont think this is a matter of life or death for them. Moving them to a different location is not an option unfortunately.

[AntsLuxembourg]

I couldn't find anything in regards to their hibernation temperature. But what I know is that it's best to keep the ants in hibernation and not just introduce them to such temperature shifts which might harm the colony. :/
You can try to use the mini fridge on a higher setting so it is around 13°C. Unless your mini fridge can't provide this temperature. Could you check what the temperature is on the different settings?