  We propose and analyze a high-fidelity hot gate for generic spin-resonator
systems which allows for coherent spin-spin coupling, in the presence of a
thermally populated resonator mode. Our scheme is non-perturbative, applies to
a broad class of physical systems, including for example spins coupled to
circuit-QED and surface acoustic wave resonators as well as nanomechanical
oscillators, and can be implemented readily with state-of-the-art experimental
setups. We provide and numerically verify simple expressions for the fidelity
of creating maximally entangled states under realistic conditions.
