Absolutely, temperatures be cooler after Phoenix. You will be further north and gaining in elevation. Typical high temperatures should be in the 90s in Phoenix. In Bryce Canyon (for example) they will likely be in the 60s and cold at night (in the 30s). You may even see snow on the ground at higher elevations.
Your best bet is to go to weather.com and search for weather at various locations on the tour. They have a monthly tab, which you can set to May to see typical average high and low temperatures. When you get close to your trip, do the same for a 10 day forecast to get more specific information.
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Your best bet is to go to weather.com and search for weather at various locations on the tour. They have a monthly tab, which you can set to May to see typical average high and low temperatures. When you get close to your trip, do the same for a 10 day forecast to get more specific information.