Let me distill a number of relevant things others said into one ordered post.
The amount of lift a plane can generate at any speed is dependant on the "density altitude". That is a calculated altitude that depends, among other things, on temperature and altitude. When the density altitude increases, as it does on a hot day, a plane will require more runway to accelerate to a speed that produces sufficient lift for flying. If there isn't enough runway there for a plane to accelerate, have an engine fail at the critical moment, and either stop or take off as appropriate, then the pilot cannot attempt the takeoff.
The easiest factor for the pilot to manipulate in this situation is takoeff weight. If the plane is lighter, less lift is required. This may give the pilot the option of taking off with fewer passengers, less baggage/cargo, or less fuel. This explains all of the behavior you are likley to see. Sometimes (particularly on small t-props) the airline will not load all the baggage. Other times, they will seek passengers to take a later flight. Yet other times, they will take off with less fuel ... leading to the extra fuel stop on some trips.
The choices for any given aircraft are laid out in a series of performance tables for each aircraft. There is not, therefore, a single magic temperature, although I can certainly imagine that when the temperature gets over 120 degrees in Phoenix, there aren't very many planes that could possibly take off.
This also explains why you don't see very many t-props flying out of Denver. Most tprops don't have enough power to carry sufficient revenue generating loads out of the mile high city in the summer.
Tom