The western express is a great route! We did it in July a few years ago. It was hottest in Utah, peaking in Hite at 115 degrees. Most cyclist we ran into had experienced difficulty with water, despite their previous considerable experience. I agree with most of roadrunner's suggestions, but we definitely found it advantageous to ride at night. We would start riding between 3am and 5am when we had a long day and heat was expected, with head and tail lights. With this strategy we could finish around 11am to 1pm. Even so, it could be getting quite hot by then. The traffic in Utah and Nevada is very low before sunrise. I remember about 1 truck per hour on highway 50, and no cars. Unfortunately this condition generally does not last after sunrise. However, on the Milford to Baker section that was about the peak traffic in the morning. I would also reiterate rr's recommendation to be self sufficient. Other cyclist told us of needing help and not being able to get any motorist to stop. If you can hit a full moon as we did there is a lot of natural light. On long days when heat was expected we carried between 1.5 to 2.0 GALLONS of water EACH, we never ran out. This amount of water might not have been sufficient if we didn't get so much of our riding done in the early am. While we prefer to camp, in Nevada we mostly got rooms. We found zero water between towns most of the way from Milford, UT across most of Nevada. So you are pretty much forced to stay in town, rooms are often quite cheap, and AC is nice! Of course if you are not constrained to ride in July or August you should have an easier time with the heat. One last warning, rattlesnakes! We saw a few on the road in Utah, some alive. One buzzed at my wife as she rode by. Keep your eyes open. Certainly be careful when you step off the road if there is brush obscuring your view of the ground, or wait for a lonely moment and stay on the road. We saw one scorpion on the road, dead.
Despite all that, for those that are prepared, this is a beautiful and enjoyable route. It is one of my favorites.