When two bodies which are near to each other have different temperatures, the hotter one emits calorific energy and the colder one absorbs it, until both reach an equal temperature.

In an ideal case, with a system formed exclusively by two bodies isolated from the rest of the universe, the energy lost by one is equal to that gained by the other.

The exchange of energy is proportional to the difference in temperature between the bodies.  For this reason as the temperatures get closer, the process gets slower.

When the two bodies are in the same state, the equilibrium temperature is determined by: m1·c1·(t1-te) = m2·c2·(te-t2) where m, c and t are the mass, the specific heat and the initial temperature of the hot body (with subscritp 1) and the cold body (with subscript 2) while te is the equilibrium temperature.

When the bodies present different physical states, the energy exchange equations must take into account the heat used to partially or totally change the state of one of the two bodies.