Babies overheat in their sleep because they are covered up with too many blankets, according to new research.nThe study found that infants who overheat are nearly three times as likely to die as those who don’t and that overheating was the cause of death in almost two-thirds of SIDS cases. It is therefore strongly recommended that babies are not covered up with extra blankets and that parents should use thin sheets and light clothing to keep them cool.