Don't know how they would tolerate extreme heat, but Bryum argenteum and Ceratodon purpureus are adapted to very dry environments and full sun.

If you are looking for something to stay green then forget about any moss for your area. Even the desert mosses go dormant in summer and turn brown to black in color. You may have to settle for a non-moss plant if you want a green cover plant. Sagina or a Sedum might be more suitable to your requirements.

Here is a link that might be useful: Marlays Garden with a tiny sedum

Unfortunately, both Sagina and Sedums conk out in the summer, here. 'Elfin' thyme does fairly well, here, but I was hoping for some thing more "fuzzy-mound-like", as well as expanding the palette. Turning black in the summer is alright, as long as it comes back fairly consistently.
Lycopus, I'm going to investigate the species you suggested, and if I ever find out what species the black moss I find growing under the creosote bushes around here is, I'll let the forum know.
Thank you both very much! : ])

You may want to check out Grimmia as it is a desert plant but probably in the mountains where it is cooler.

Here is a link that might be useful: USDA section on Grimmia species

I agree with lycopus ; Bryum argenteum is my favorite moss. It is hardy for extreme heat and cold. It even grows in Antarctica! This moss is found almost anywhere you go in the world. It is my choice for bonsai. It is very tolerant of the fertilizers you might use on your plants. If you see moss growing between the cracks of concrete in hot pavement, it is probably Bryum argenteum. Plant clusters you gather from the wild or let your pieces you gather dry up. Crumble them over the tops of your pots. Make sure you don't water so heavy the moss floats out. It takes hold very fast on older Bonsai soil where the bark in the soil is breaking down. When this moss grows new tips; you can brush them of into another pot to get growth. These take hold very quick.