A Bat in the Basement

It's the dead of winter, and a cold, snowy winter it has been thus far. The finished part of our basement is unheated - which is a bit strange considering that the unfinished part is - and so it's been hovering at a frosty 10 - 11 degrees.
And yet the other night we had a bat swooping around our rec room.
I thought that bats hibernated during the winter! And I know that they will often hibernate in the attic, but there is no access from our attic to our basement (that I know of). So how did it get downstairs in the first place and why is it awake in the second?
Max thought it was because the dogs were downstairs with us, and barking as they played ( so maybe they woke it up??). And it had been quite mild (it almost got up to 0 outside), so maybe the bat got confused and woke up thinking it was spring?
I managed to get it back into the unfinished part of the basement and shut the door, but now I don't know what to do with the poor bat. I think that if we catch it and put it outside, it will freeze. I'm not crazy about leaving it in there, because I'm pretty sure that bat droppings aren't good for us (and I don't want to find them in the boxes I've got stored down there!).
Now the problem is that I can't find it! There are windows in that part of the basement, and so it's really bright during the day. I've gone looking (in a timid sort of fashion) but can't seem to find it hanging anywhere. So maybe my dilemma is moot point, but that's no solution.....