The Peltier coefficient describes the amount of heat that is carried by an electrical current when it passes through a material. When two materials with different Peltier coefficients are placed in contact with one another, the Peltier effect causes a net flow of heat either towards or away from the interface between them. Spintronics describes the transport of electric charge and spin angular momentum by separate spin-up and spin-down channels in a device. The observation that spin-up and spin-down charge transport channels are able to transport heat independently of each other has raised the possibility that spin currents could be used to heat or cool the interface between materials with different spin-dependent Peltier coefficients. Here, we report the direct observation of the heating and cooling of such an interface by a spin current. We demonstrate this spin-dependent Peltier effect in a spin-valve pillar structure that consists of two ferromagnetic layers separated by a non-ferromagnetic metal. Using a three-dimensional finite-element model, we extract spin-dependent Peltier coefficients in the range -0.9 to -1.3 mV for permalloy. The magnetic control of heat flow could prove useful for the cooling of nanoscale electronic components or devices.