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Thank you for this great information. I'm trying to figure out how to protect them as well. Lots of coyotes and sun so I feel they need to be in a covered run - not sure how to protect them from snakes etc. if necessary. Not sure if I need to dig a coop barrier???Glad to meet you, and welcome to BYC. Congratulations on your new desert home!
Two Crows has some real experience with desert chicken keeping. But last summer, we had a lot of heat up here in New England, and I adopted the Texas Chicken Air Conditioner. It was an idea discussed here, and it's pretty simple. You take jugs (or bottles) of water and put them in your freezer. Then just set them out in the coop or pen in a shaded area. My chickens (and quail) appreciated it. They all sat around those cold bottles as they melted, and just luxuriated in the coolth.
You will want to build your coop to match your environment, with lots of ventilation, wherever you are. Here is a handy article about ventilation that has links to a number of coop designs for different climates. It's funny but also very clear.
You will also want to choose breeds of chicken that are heat tolerant. Many breeds are good at both heat and cold, but a few are especially good at hot weather. You may simply want to ask around in your area about the breeds that are favorites, and maybe you'll find somebody ready to sell you some eggs or chicks. Be careful about choosing who to buy from, though. Look at the cleanliness and care of the facility. There are a lot of lists of heat tolerant chicken breeds online, but many disagree. There are breeds that come from hot lands, and that might be a good clue. But another clue is the size of the birds' earlobes, comb and wattles, which will help dispel their body heat. Less fluffy down is another characteristic of hot climate birds. Here is a list and discussion that seems pretty on target, but I have not kept chickens in hot climates. Also, keep in mind Two Crow's point about the cold nights in desert climates. Watch what happens in your area this year!
Lastly, about chickens and yards/gardens. They can coexist, but you really have to think chicken to make it work! Probably fencing is the best solution to keep part of your yard looking decent because chickens just wreak havoc on plants. They love to eat grass and all sorts of weeds, herbs and almost any plant. But they also love to eat bugs. They scratch which can destroy plants they don't eat, but may also be helping to aerate the soil and dig compost down in. You have to figure out how to make the plusses out weigh the minus parts.
Part of your solution may lie in how many chickens over how much space, because I had 4 chickens in a 12 X 9 foot pen that was filled with full grown mugwort, goldenrod, grasses, and even milkweed. The only plants that survived the chicken onslaught were a few beat up pokeweed plants. I didn't think anything would eat mugwort or milkweed! The chickens seemed none the worse for however much they ate of that stuff.
If you are getting light weight chickens for the desert, you may need fencing taller than the 4 foot fencing that has been discussed by more well-watered chicken keepers, in order to protect the parts of your yard. Or if the chickens are happy with the allotment they have, and don't feel over crowded, they may not try to fly over a 4 foot fence. I have fairly mature bushes that they leave alone, but when I start my spring garden, the chickens are going to be shut out! They are welcome to come scratch in the fall after I take down the plants. Or maybe when supervised, to look for bugs on my well-grown vegetables.