Redworms can survive in compost temperatures ranging from 32-95 degrees, as long as there is enough depth to allow them refuge from temperature extremes on the surface.
In cold climates, you'll want to thicken and insulate your compost to keep the center warm. Adding aerobic bacteria will generate more heat as well. Aerobic bacteria feed on carbon and nitrogen, gaining their energy by oxidizing organic material. That oxidation process heats the compost. As a bonus, they become food for your Redworms once they die.
If you're using a compost bin, try storing it in a garage or basement. This will allow you to control temperature regulation. For an outdoor compost, covering with a tarp will help reduce heat loss.
In hot climates, you'll want a compost depth of at least 8". This will help provide enough insulation to protect your worms as the surface layer of soil heats. Be sure to water your compost regularly, during cooler hours of the day.
If possible, cover your compost with a clear plastic sheet. This will also help combat heat, though be sure not to completely cut off airflow; Redworms need oxygen too!