Thermal Equilibrium and Temperature

When two bodies at different temperatures are brought into contact through a wall that conducts heat (called a diathermic wall), heat flows spontaneously from the hotter body to the colder one until, after some time, no further net change in either body's macroscopic state occurs -- both bodies are then said to have reached thermal equilibrium with each other. At thermal equilibrium, quantities such as pressure and volume of each body settle down to steady values and stop changing with time, even though heat may still, in principle, be flowing back and forth at the molecular level -- it is the net flow that becomes zero.

Temperature is precisely the physical quantity whose equality between two bodies signals thermal equilibrium, and whose inequality determines the direction of spontaneous heat flow: heat always flows from the body at higher temperature to the body at lower temperature, never the other way round on its own. This makes temperature fundamentally different from quantities like pressure or volume, which do not by themselves determine the direction of any spontaneous flow. …