The most important thing to remember when travelling to Denver is this: Denver and the mountains do not have the same weather. Some people seem to equate all weather in Colorado with Denver, but that's not the way it works. Denver is around 5280' in elevation while Leadville is around 10,000' and the ski resorts are even higher. In the winter, there may be massive snow storms going on in the mountains and ski resorts, while Denver is dry as a bone.
In general, Denver is HOT from June through August--hot like over 90 degrees F. Some people will tell you that the temperature drops at night, but in my experience, living right in the city where we have a true heat island, is that even when the temps drop, it can still feel pretty hot. You'll find that wherever you have more vegetation and less pavement you will have more of a temperature decrease at night. During the summer, we also tend to have thunderstorms almost every day. Anytime after noon they roll in and clouds begin to build. The resulting storms are almost always more severe east of Denver where they seem to pick up strength as they head away from the mountains.
On the other hand, July and August are the only two months of the year when you can visit some of Colorado's most spectacular high country--as there may be snow through June in some places. So don't avoid Denver in the summer, just be prepared for the weather.