An organism is thought to be in a dynamic state of homeostasis when each physiological and behavioral system reaches a delicate balance within the framework of other regulatory processes. Many biological systems target specific set-point variables and generate circadian patterns. In this article, we focus on specific measurements representative of two systems, namely deep-body temperature and activity counts. We examine data collected every 30 minutes in mice, assume there are underlying circadian patterns, and extend the approach presented in Brumback and Rice (1998, Journal of the American Statistical Association 93, 961-976) in order to obtain estimates in the presence of correlated data. We then assess homeostasis using these estimates and their statistical properties.