I'm not sure how much heat is lost through the basement wall and out the bottom of the slab - I've seen widely varying estimates from different rules of thumb, sources, and calculators.
This article points to a DOE study finding a relatively meaty $300-400 of savings per year, but it points to a broken link so we can't examine its logic. The LBL energy savor calculator seems to think
not much in the case of my house, even with the top insulated well and the basement insulated not at all, while many sources quote
20-
30% and
this calculator had incredible levels of heat loss far above my house's actual consumption just through the basement. My suspicion is that the correct answer is "not much heat at all" given the small temperature deltas between underground and conditioned air and given that recommendations and codes call for very little insulation even in new construction.
Not sure what sort of basement I have in terms of the question. It's 2/3 of the footprint of the house, so around 800 sq ft, with poured concrete walls and floor, no insulation under the slab, no insulation on the outer walls. One room is badly finished (badly enough we don't feel bad about taking it apart someday) and the remainder is unfinished. My house was built 1969 and I have an efficient natural gas furnace today with an eye towards an air source or ground source heatpump when it dies if not before. I've insulated walls and attics, air sealed the house and ducts, and gotten ceiling fans, so I'm out of 'low hanging fruit' projects.
The theoretically correct answer is to dig a trench on the outside of the basement, put on insulation and waterproofing out there, and then fill it back in. That's prohibitively expensive out here in the real world, so the next best answer is to insulate the inside. In an above-grade wall you want the wall to dry outwards so you have a vapor barrier - in a below grade wall the water is coming from the outside, so all you can do is 1) put in a vapor barrier to trap a bunch of moisture and mold right on the outside of the vapor barrier, or 2) use no vapor barrier, moisture permeable insulation like rock wool polystyrene, and moisture rated (purple or green) drywall. If you put foam in, you have to cover it with a fireproof layer (drywall) to be up to code, so I think that means do nothing until you're ready to finish the basement - and for us that involves an egress window and moving the HVAC system a bit, so it's longer term project.
This article is very, very good. There's also a ton to read
here, not just on basements...