The achievement of local cooling is a prominent goal in the design of functional transport nanojunctions. One generic mechanism for local cooling is driving a system through a local uphill potential step. In this talk we examine the manifestation of this mechanism in the context of the Kramers barrier crossing problem. For a particle crossing a barrier, the local effective temperature and the local energy exchange with the thermal environment are calculated, and the coefficient of performance of the ensuing cooling process are evaluated. These results represent a heuristic demonstration of a mechanism for pumping heat in a nanosystem.