Good question. I'd be happy to help.
So first off there's 2 temperature benchmarks to look at and pay attention to. The first one is where the freeze is, 30 degrees-ish. You know that one. And its good you know that.
But the second one is just important, and that is roughly 50 degrees. This second temperature is a benchmark for where growth slows down. Now it doesn't stop there. But for many organisms, both plant, animals, insect, bacteria that's where things slow down a lot. This is why your fridge works also (cool right?!) Many fridges operate around that temperature.
You could put the potato bags in your basement at night. (Reverse greenhouse?) And then put them out during the day. (It may also interest you to know that the coldest part of the night is around the period of 5 to 7 AM).
Both soil bags and buckets can work. But, its my experience that sometimes they don't do well if the temperature gets too high (I'm in the southwest). It can be difficult to get them to work right. But give things a try. (You are in a different climate than I am). There are also ways to store vegetables outside also.