Access to Crawlspace from Basement
It appears in your case that the crawl space was insulated and received its heat from the basement. From your description, it sounds like the floors above the crawlspace are also insulated or the area probably would not have frozen.
To reduce heating costs, the better approach would be to insulate the pipes and possibly add heat tape to vulnerable pipes near outside walls or exposed to drafts. The cost of pipe insulation will be much less in the long run than heating the unused space.