So I have been thinking about what it would mean to have a high temperature. This means the the change in entropy per change in energy is very low. But what does this mean combinatorically? For instance, take a canonical ensemble of N atoms and U energy. When is temperature high? I have feeling that it must be when U>>N but I'm not sure why. Maybe it's wrong. Can anyone explain what a high temperature corresponds to in terms of how many atoms you have compared to how much energy?