We demonstrate sharp thermally induced switching between ferromagnetic and antiferromagnetic RKKY (Ruderman-Kittel-Kasuya-Yosida) exchange in a spin-valve with the spacer incorporating a thin diluted ferromagnetic layer as the core. We illustrate the mechanism behind the effect as being due to a change in the effective thickness of the spacer induced by the Curie transition into its paramagnetic state. The ability to switch between ferromagnetic and antiferromagnetic states in a magnetic multilayer by a slight change in temperature may lead to new types of spin-thermoelectronic devices for use in such applications as memory or oscillators.