Charlotte,
Your temps are still fine for that squash. I would leave them on the vine until the skin is too tough to puncture with a fingernail. The only curing I've ever heard of, for squash, is perhaps to wipe them down with a light disinfectant, to prevent possible spoilage. But I myself have never done that with my squash. Cooler temps, but above freezing seem best for storage. But when pinched for space I've used them for doorstops, stashed them behind the couch and under the bed! Hubbards are renowned for storing well. But, if, after say, four or five months, you still have quite a few unused squash, you might consider cooking some up and either freezing or canning in order to ensure the longest possible use of your harvest. That's what we're going to do this year.

George
Tahlequah, OK