Evidence is gradually accumulating in support of the hypothesis that a process of thermostatic brain cooling and warming underlies sleep cycles, i.e., the alternations between non-rapid-eye-movement and rapid-eye-movement sleep throughout the sleep phase of the sleep-wake cycle. A mathematical thermostat model predicts an exponential shape of fluctuations in temperature above and below the desired temperature setpoint. If the thermostatic process underlies sleep cycles, can this model explain the mechanisms governing the sleep cyclicities in humans? The proposed nested doll model incorporates Process s generating sleep cycles into Process S generating sleep-wake cycles of the two-process model of sleep-wake regulation. Process s produces ultradian fluctuations around the setpoint, while Process S turns this setpoint up and down in accord with the durations of the preceding wake phase and the following sleep phase of the sleep-wake cycle, respectively. Predictions of the model were obtained in an in silico study and confirmed by simulations of oscillations of spectral electroencephalographic indexes of sleep regulation obtained from night sleep and multiple napping attempts. Only simple-inverse exponential and exponential-functions from the thermostatic model were used for predictions and simulations of rather complex and varying shapes of sleep cycles during an all-night sleep episode. To further test the proposed model, experiments on mammal species with monophasic sleep are required. If supported, this model can provide a valuable framework for understanding the involvement of sleep-wake regulatory processes in the mechanism of thermostatic brain cooling/warming.