Whew, if you are from Yuma, you really do know about the heat, and have a setup for desert hiking. The main difference is that there is no shade at the bottom of the canyon, not even a creosote to wiggle under (that's why I recommend the tent fly for shade, rather than the main body with netting... you don't even need a tent at night.)

You can put the treadmill at an incline and turn around and walk; I have friends who do this for running. Step-downs (as well as step-ups) with weights / backpack are good practice - and you might be surprised at the difference in strength between your legs. Walking down real stairs, at a stadium. Long series of strength moves - such as single-leg bodyweight squats, or yoga - to develop muscle flexibility and endurance. Also work on building up side leg muscles - adductors and abductors - since biking essentially ignores these. The machines are dangerous, use a low pulley or exercise bands instead (GoFit ProGym is a good home/travel set and only about $25.) The best thing is hiking though!

As a geologist I've done quite a lot of work in the desert; heat really does make one stupid, so I've learned to keep an internal running commentary on what I am doing and what state my body is in, which also helps for recreational hiking.