<p>This numerical work presents the application of two particle filters used as an observer and a controller during the mild hypothermia systemic treatment of the hypoxic-ischemic encephalopathy in neonates. The bioheat transfer model developed in our previous studies was used here for the joint solutions of the state estimation and predictive control problems. Based on clinical practice for this kind of treatment, measurements were supposed to be available for the deep body temperature, as well as for the temperatures over the skins of the head and abdomen. The temperatures inside the brain and on the back surface of the abdomen were controlled, together with the deep body temperature, through the manipulation of the external heat flux to a mattress placed under the patient. The results presented below reveal that the algorithm used in this work was capable to drive the controlled temperatures to the desired setpoints, during the cooling and rewarming phases of the treatment. Therefore, it has great potential to be used in actual clinical practice, especially to control the brain temperature during the mild hypothermia treatment promoted by systemic cooling.</p>