A neonatal enteral feeding system for delivering neonate fluid is disclosed. The system includes a cooling unit for cooling the breast milk before, during and after a feeding cycle to mitigate unwanted bacterial growth and reduction of fat content in the breast milk. The system also includes a warming unit for heating the cold breast milk to a temperature above room temperature (preferably, standard body temperature) so that the neonate can focus his or her energy on healing, growth and digestion instead of heat generation. Additionally, the system has a peristaltic pump which draws the breast milk from a bottom side of the container and the container is vented so as to be capable of delivering all of the breast milk in the container to the neonate.