I would give it a shot since you already have the crate. I'll second a pet heating pad to make it cozy if it's not too expensive.
Also, I am not sure if this will help but when my older girl was having litterbox issues I used Cat Attract litter, which was expensive as all get-out but helped get her back in the habit.
Also, I am not sure if this will help but when my older girl was having litterbox issues I used Cat Attract litter, which was expensive as all get-out but helped get her back in the habit.