  In four space-time dimensions General Relativity can be non-trivially
deformed. Deformed theories continue to describe two propagating degrees of
freedom, as GR. We study Euclidean black hole thermodynamics in these
deformations. We use the recently developed formulation that works with SO(3)
connections as well as certain matrices M of auxiliary fields. We show that the
black hole entropy is given by one quarter of the horizon area as measured by
the Lie algebra valued two-form MF, where F is the connection curvature. This
coincides with the horizon area as measured by the metric only for the case of
General Relativity.
