Although brain temperature has neurobiological and clinical importance, it remains unclear which factors contribute to its daily dynamics and to what extent. Using a statistical approach, we previously demonstrated that hourly brain temperature values co-varied strongly with time spent awake (Hoekstra et al., 2019). Here we develop and make available a mathematical tool to simulate and predict cortical temperature in mice based on a 4-s sleep–wake sequence. Our model estimated cortical temperature with remarkable precision and accounted for 91% of the variance based on three factors: sleep–wake sequence, time-of-day (‘circadian’), and a novel ‘prior wake prevalence’ factor, contributing with 74%, 9%, and 43%, respectively (including shared variance). We applied these optimized parameters to an independent cohort of mice and predicted cortical temperature with similar accuracy. This model confirms the profound influence of sleep– wake state on brain temperature, and can be harnessed to differentiate between thermoregulatory and sleep–wake-driven effects in experiments affecting both.