This is a prospective, single center, pharmacokinetic study of intravenous hydrocortisone therapy for systemic low blood pressure during hypothermia treatment in asphyxiated newborns. Patients will be allocated to hydrocortisone supplementation while receiving conventional inotropic therapy as needed. The hypothesis is that a detailed study of hydrocortisone pharmacokinetics during therapeutic hypothermia would help to personalize steroid supplementation in asphyxiated neonates. As the overall metabolic rate decreases with lower body temperature, drug metabolism is likely to be reduced as well, and lower doses, or less frequent dosing will be sufficient to achieve the targeted steroid range and biological effects in asphyxiated neonates with relative adrenal insufficiency. Thus, the investigators are planning to measure initial, baseline serum cortisol levels and serial serum cortisol levels after hydrocortisone supplementation in cooled asphyxiated neonates.