A friend and I left Alabama on July 5, 2010 and rode the Continental Divide Trail from Silver City, New Mexico, to Silver Gate, Montana. We started back to Alabama the last week of July.
After leaving Silver City the further north we went the cooler it was in the mornings. By the time we got into Colorado we would layer up in the mornings, remove clothing by mid-morning, layer up again when crossing a pass, and then un-layer again as we worked our way down the mountains.
Each night we found a motel - sometimes a fairly modern venue like Holiday Inn Express, and other times a 1950's throw-back that was a roof and a cot and that was all. We took camping gear in case we got stuck in the boonies but never had to use it.
Your best window for "warm" weather will be late July through August, but at the higher elevations you can still encounter dangerous cold, snow, and other precipitation. On a different trip, it snowed on my family and me on June 21, 2004, at Tin Cup Pass, CO.
Preparedness, alertness, and flexibility will be your friends. Which I guess means that at the end of the day, you have to be your own best friend for such an outing.
Current rides: 2001 GL1800, 2014 DL650 Adventure; Gone away: 5 BMW's, 4 Honda's, 2 Suzuki's
"The object of life is not to be on the side of the majority, but to escape finding oneself in the ranks of the insane." -Marcus Aurelius