  We consider single interval R\'enyi and entanglement entropies for a two
dimensional conformal field theory on a circle at nonzero temperature. Assuming
that the finite size of the system introduces a unique ground state with a
nonzero mass gap, we calculate the leading corrections to the R\'enyi and
entanglement entropy in a low temperature expansion. These corrections have a
universal form for any two dimensional conformal field theory that depends only
on the size of the mass gap and its degeneracy. We analyze the limits where the
size of the interval becomes small and where it becomes close to the size of
the spatial circle.
