Summary. Caloric restriction (CR) has been shown to delay the onset of cancer and other diseases that are associated with aging. Currently there are very few studies examining the whole-animal physiological response to late onset CR. We study the ways by which mice physiologically compensate for reduced availability of food given exposure to late onset CR and compare these with mice fed ad libitum. The data arise from a 70-day experiment that was undertaken by the authors. A joint model is developed to describe core body temperature and levels of activity and the model parameters assessed for temporal dependence by using dynamic linear models. A Bayesian approach is used throughout. The dynamic parameters are shown to be plausibly constant over time and the constant parameter model is then embedded within a random-effects structure to explore differences between the responses of CR and ad libitum mice. This model is shown to provide a good description of the data.