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 Renyi 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.
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