  We generalize techniques previously used to compute ground-state properties
of one-dimensional noninteracting quantum gases to obtain exact results at
finite temperature. We compute the order-n R\'enyi entanglement entropy to all
orders in the fugacity in one, two, and three spatial dimensions. In all
spatial dimensions, we provide closed-form expressions for its virial expansion
up to next-to-leading order. In all of our results, we find explicit volume
scaling in the high-temperature limit.
