In this chapter we define, in terms of the entropy functions derived in the previous chapter, two temperature functions, showing that they exist and are continuous with respect to all the state variables. The full four-member t-type classification of systems is defined according to whether the internal energy and entropy are decreasing or increasing in adiabatic processes, relating these properties to the signs of temperature and heat capacity. We show that the bounds on temperature are the same for all systems of the same t-type and that the condition for two systems to be in mutual thermal equilibrium is that they are at the same temperature. Thermometers and reservoirs are defined and discussed.