Chandra and XMM-Newton observations of many clusters reveal sharp discontinuities in the surface brightness, which, unlike shocks, have lower gas temperature on the X-ray brighter side of the discontinuity. For that reason these features are called ``cold fronts. It is believed that some cold fronts are formed when a subcluster merges with another cluster and the ram pressure of gas flowing outside the subcluster gives the contact discontinuity the characteristic curved shape. While some edges may not arise directly from mergers (e.g., A496, Dupke & White, 2003), this paper focuses on those which arise as contact discontinuities between a merging subcluster and the ambient cluster gas. We argue that the flow of gas past the merging subcluster induces slow motions inside the cloud. These motions transport gas from the central parts of the subcluster towards the interface. Since in a typical cluster or group (even an isothermal one) the entropy of the gas in the central regions is significantly lower than in the outer regions, the transport of the low entropy gas towards the interface and the associated adiabatic expansion makes the gas temperature immediately inside the interface lower than in any other place in the system, thus enhancing the temperature jump across the interface and making the ``tip of the contact discontinuity cool. We illustrate this picture with the XMM-Newton gas temperature map of the A3667 cluster.