  We calculate thermal corrections to R\'{e}nyi entropies for free massless
fermions on a sphere. More specifically, we take a free fermion on
$\mathbb{R}\times\mathbb{S}^{d-1}$ and calculate the leading thermal correction
to the R\'{e}nyi 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
R\'{e}nyi 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 R\'{e}nyi entropies.
