  We propose an energetic interpretation ofstochastic processes described by
Langevin equations with non-uniform temperature. In order to avoid
It\^{o}-Stratonovich dilemma, we start with a Kramers equation, and derive a
Fokker-Plank equation by the renormalization group method. We give a proper
definition of heat for the system. Based on our formulations,we analyze two
examples, the Thomson effect and a Brownian motor which realizes the Carnot
efficiency.
