The temperature is more important than light. You want to keep the plant as cool/cold as possible in your basement, 32-50F would be ideal. You don't want to overwater, but give it a bit of water once every 3 or so weeks. Light isn't necessary if it's truly dormant. Then in the early spring, cut it back and get it outside, gradually exposing it to light.

I keep container clematis (big and small) in my unheated garage. I put them in boxes of styrofoam peanuts or leaves to keep the pots insulated against freeze/thaw cycles with a light covering on top. It can get well below freezing there and I've never had a problem. I barely water them. They get some light through a window.