We compute thermal corrections to R\'enyi entropies of d dimensional
conformal field theories on spheres. Consider the nth R\'enyi entropy for a
cap of opening angle 2θ on Sd−1. From a Boltzmann sum
decomposition and the operator-state correspondence, the leading correction is
related to a certain two-point correlation function of the operator (not equal
to the identity) with smallest scaling dimension. More specifically, via a
conformal map, the correction can be expressed in terms of the two-point
function on a certain conical space with opening angle 2πn. In the case of
free conformal field theories, this two-point function can be computed
explicitly using the method of images. We perform the computation for the
conformally coupled scalar. From the n→1 limit of our results, we extract
the leading thermal correction to the entanglement entropy, reproducing results
of arXiv:1407.1358.Comment: 18 pages, 5 figures; v2 reference adde