Summer squash are usually not stored but can be held in the refrigerator in a plastic bag for about 2 weeks.
Winter squash harvested without a stem will not store well. Before being put in the storage area the fruits must be cured. The area used for curing should have a temperature of 75 to 80 degrees and good air circulation. If no other area is available put the squash near the furnace. Curing will harden the rinds and help heal wounds but not bruises.
After curing, which takes about 2 weeks, store the squash in a dry place at 55 to 60 degrees. If the temperature is greater than 60 degrees the squash will lose moisture and become stringy.
Acorn squash is not cured but if stored at 45 to 50 degrees it will keep 35 to 50 days. If acorn squash are cured, they will get stringy and dry out.