Curing is mainly drying out the skin and sealing cuts. The warmer the temperature, the faster it'll happen. High humidity is supposed to be good as well, but I don't understand why. So I guess if you're in a rush, keep them outside in the heat for a week. For a given curing time, warmth also increases sugars, but I suspect those same sugars would come about with a longer curing time and cooler temps.

Remember that, for storage, once cured, you should rub them with some dilute bleach to disinfect the surface, and many suggest rubbing a light film of oil on them as well to help the seal. My moschata last more than 6 months that way indoors.