A simple, and not too expensive, option might be to build an insulated storage space in the corner of your basement. Preferably the corner farthest from the source of heat. Not being load bearing you can go 24" stud spacing. Catching the corner, two sides of the space, increases the coupling of ground temperatures while the insulation decouples the warmth from the basement.

I suspect that a basic stud wall and R-13 insulation will do it and an interior door, I'd go with a 36" model to make loading easier, will be adequate. If you go with an interior door apply suitable weatherstripping and a threshold to seal the opening.