How cold can mash safely get, and advice on warming?

[Horus92]

It's cold where I live and I'm having a lot of trouble keeping the mash warm.

How cold can mash safely get, and what can I do to warm it up?

I keep it in a filing cabinet at night and pack the thing full of blankets but it still ends up a little chilly in the morning, and it never warms up in the day even if I leave it sitting on a heating vent all day.

The yeast is still alive (it may have died in one container actually, dunno), but I don't know how long it can survive these temps.

I dont' know how cold the water is, haven't been able to find my thermometer. What's the coldest it can safely get?