  We investigate a mechanism for cooling a lead based on a process that
replaces hot electrons by cold ones. The central idea is that a double quantum
dot with an inhomogeneous Zeeman splitting acts as energy filter for the
transported electrons. The setup is such that hot electrons with spin up are
removed, while cold electrons with spin down are added. The required
non-equilibrium condition is provided by the capacitive coupling of one quantum
dot to the shot noise of a strongly biased quantum point contact in the
tunnelling limit. Special attention is paid to the identification of an
operating regime in which the net electrical current vanishes.
