Anne, I hope our Floridians will give you advise regarding temperature.
In the meanwhile, since I really don't know much about Spathoglottis ( I have never grown any of these) I looked it up. It seems the Spathoglottis parsonii is not an accepted name, its correct name is Spathoglottis x parsonsii, and it is a natural hybrid.
http://apps.kew.org/wcsp/named...
Perhaps this will make it a bit easier to gather information….
and
http://www.orchidspecies.com/s...