If a baby falls asleep with a fever of 38.7 degrees, it is because the child is more sleepy and tends to appear depressed, which is instead more serious; it is less serious if it is in a normal sleep state. A fever of 38.7 degrees requires the child to be treated with antipyretic methods. If the child’s mental state is good, you can use physical cooling methods to reduce fever, such as using a warm towel to wipe the baby’s whole body skin. If the child falls asleep because of drowsiness and is not in good spirits, oral antipyretic drugs such as ibuprofen suspension or acetaminophen suspension are needed. You need to take your child to the hospital quickly for a specific examination to check the cause of the fever and treat the cause so as not to delay the child’s condition. If the child’s fever is not too severe and the temperature is slowly going down, there is no need to worry too much. If the temperature continues to rise, it is safer to hospitalize quickly for treatment.