Much of black hole thermodynamics is limited to systems with a high degree of symmetry. In this talk, I will discuss a non-stationary, non-axisymmetric black hole spacetime that nevertheless admits a standard thermodynamics: a black hole corotating with an orbiting moon. More precisely, we consider a Kerr black hole perturbed by a particle on the circular orbit whose frequency matches that of the event horizon. The key point is that the spacetime has a helical Killing vector that generates the event horizon, allowing the surface gravity to be defined in the standard way. The surface gravity is uniform on the horizon and should correspond to the Hawking temperature of the black hole. We calculate the change in surface gravity/temperature, finding it negative: the moon has a cooling effect on the black hole. We also calculate the area/entropy of the perturbed black hole, finding no change from the background Kerr value.