Your plastic should tolerate the heat. There are others who live in Bama that have workshops set apart from their homes and they don't seem to register many complaints.
What is the humidity level like during the hot times? I'd keep an eye on humidity issues like micro bubbles and if they become a problem I'd keep the plastic in the house when perhaps a dehumidifier is keeping the moisture levels in check. Sometimes its more convenient to store larger containers of plastic in the house and fill smaller ones to take out to the shop area, but the only issue I can see with Alabama in the summer and plastic storage in a work shop would maybe be high humidity.