Thermal corrections to Renyi entropies for free fermions

We calculate thermal corrections to Renyi entropies for free massless fermions on a sphere. More specifically, we take a free fermion on R x Sd-1 and calculate the leading thermal correction to the Renyi entropies for a cap like region with opening angle 2 theta. By expanding the density matrix in a Boltzmann sum, the problem of finding the Renyi entropies can be mapped to the problem of calculating a two point function on an n sheeted cover of the sphere. We follow previous work for conformal field theories to map the problem on the sphere to a conical region in Euclidean space. By using the method of images, we calculate the two point function and recover the Renyi entropies.