We show that a star orbiting close enough to an adiabatically grown supermassive black hole (SMBH) can capture weakly interacting massive particles (WIMPs) at an extremely high rate. The stellar luminosity due to annihilation of captured WIMPs in the stellar core may be comparable to or even exceed the luminosity of the star due to thermonuclear burning. The model thus predicts the existence of unusual stars, essentially WIMP burners, in the vicinity of a SMBH. We find that the most efficient WIMP burners are stars with degenerate electron cores, e.g. white dwarfs (WDs); such WDs may have a very high surface temperature. If found, such stars would provide evidence for the existence of particle dark matter and can possibly be used to establish its density profile. On the other hand, the lack of such unusual stars may provide constraints on the WIMP density near the SMBH, as well as the WIMP-nucleus scattering and pair annihilation cross-sections.