Can redworms live in the extreme temperatures "Hot" or "Cold"?
Absolutely! Underground or in a compost system conditions are much different from the outside temperatures. You just need to assist your redworms by making their home livable.
In cold climates; there are several solutions and the main objective is to keep the redworms from freezing. Insulate with compost is the first choice. If your ground freezes in the winter then you need to have your compost thick enough to keep from freezing in the middle. I have often harvested redworms in the cold weather and I can find them just under the frozen part of the compost.
Another solution is to have an aerobic compost as part of the redworm compost. This is not always possible unless you can find enough green material to compost that would allow the aerobic bacteria to thrive. If you do this will often heat up your compost and your redworms will live along the heated edges and eat the bacteria as they die.
Last the other option is to bring your compost inside the garage or basement. This is a good idea since you can usually keep the area at an even temperature and above freezing.
In Hot climates; moisture and compost depth is your best way to compost.
Compost depth (8" or more) will insulate your redworms from the heat as well as it does from the cold. If you can put your compost in a shady area and make sure that your compost bin is not a dark color that would attract heat.
The moisture in your compost is a great insulator from the heat. It is the same as digging in moist soil, no matter how hot it is you only have to go a couple of inches down for the temperature to cool down.
If you do not have a shady area to put your bin cover your compost with a clear plastic so it does not attract additional heat. This will keep your moisture in the compost. Be sure not to put the plastic on so tight that it cuts off the air getting into the compost. Redworms need to breath.