  We consider Kac's 1D N-particle system coupled to an ideal thermostat at
temperature T, introduced by Bonetto, Loss, and Vaidyanathan in 2014. We obtain
a propagation of chaos result for this system, with explicit and
uniform-in-time rates of order N^(-1/3) in the 2-Wasserstein metric. We also
show well-posedness and equilibration for the limit kinetic equation in the
space of probability measures. The proofs use a coupling argument previously
introduced by Cortez and Fontbona in 2016.
