Rabbits are a good homestead source of meat, and a few can be kept on hand-harvested weeds (making sure you know what you are feeding them) plus a bit of hay and grain in the winter. They handle cold weather quite well, but suffer greatly in hot summer weather, and the bucks will become infertile for months when the temperatures go above 80 F. (It can take up to three months for their fertility to recover, once things cool off.) Here is one resource with some ideas that may help to keep rabbits cool: http://ressources.ciheam.org/om/pdf/c08/95605275.pdf

There are quite a few other ideas, but it seems like most of them require access to electricity (bottles of ice, fans blowing through a wet towel, and others) and since we are working towards being able to survive (if necessary) without power, we might get more good from the above document. Of course, it is crucially important to make sure the animals always have access to clean, cool water, and have shade, and as much breeze as may be available.