(1) Background: The field of medicine requires simple cooling materials. However, there is little knowledge documented about phase change materials (PCM) covering the range of 28 to 40 degrees Celsius, as needed for medical use. Induced mild hypothermia, started within 6 h after birth, is an emerging therapy for reducing death and severe disabilities in asphyxiated infants. Currently, this hypothermia is accomplished with equipment that needs a power source and a liquid supply. Neonatal cooling is more frequent in low-resource settings, where ~1 million deaths are caused by birth-asphyxia. (2) Methods: A simple and safe cooling method suitable for medical application is needed for the 28 to 37.5 degrees C window. (3) Results: Using empirical experiments in which the ingredients in Glauber salt were changed, we studied the effects of temperature on material in the indicated temperature range. The examination, in a controlled manner, of different mixtures of NaCl, Na2SO4 and water resulted in a better understanding of how the different mixtures act and how to compose salt solutions that can satisfy clinical cooling specifications. (4) Conclusions: Our Glauber salt solution is a clinically suited PCM in the temperature interval needed for the cooling of infants suffering from asphyxia.