In this talk I will show that when inelastic processes are involved unconventional thermoelectric effect emerges. The simplest manifestation is a three-terminal mesoscopic system. An Onsager theory on the linear transport of such a system will be derived. Anomalous "cooling by heating" and "heating by cooling" effects will appear which will be discussed via a simple microscopic hopping transport model. I will also talk about the energy efficiency and the new figure of merit as well as possible applications of the idea. Finally the theory is applied to 1D hopping systems where the mesoscopic fluctuations of thermopower will be discussed.