Although negative absolute temperatures, and rotating temperatures, only arise in certain special situations it is of interest to consider what, if any, changes have to be made in traditional thermodynamics in order to accommodate them. It is found that about the only change required is a slight modification of the Kelvin-Planck formulation of the second law. The terms, hotter, colder, and the usual procedures of thermodynamics are extended to include negative temperatures but a rigorous analysis is not attempted. The paper is more concerned to give the lay physicist an appreciation of how these ‘contemporary’ ideas fit in the older context. The ideas of negative and rotating temperature are not only useful descriptions of physical situations but they lead to considerable economy of thought in making physical predictions and in some cases lead to predictions which could hardly have been made without their use.