Thanks for the query
As per your description baby is suffering from cold stress
( a condition in which there is difference between temp. of trunk and periphery) also called as mild hypothermia
Helping your newborn to keep his body temperature normal is very important. Calories that he needs for growth can be spent trying to keep warm or stay cool. A newborn’s body temperature goes up and down quickly as the temperature around him changes. Therefore, how you dress him and where you place his crib or bassinet plays a big part in keeping your baby’s body temperature normal. If his crib is in a cool or drafty room, under a ceiling fan or air conditioning vent, your baby can lose body heat. If temp. difference is less than 2 F then its normal. Even after taking all precaution if periphery is colder and is not progressing( central part remains warm) then no need to worry as circulatory immaturity can cause this even in normal condition.
A newborn needs about 17 hours of sleep each day for normal growth; most newborns average 18 to 20 hours of sleep each day. Most babies sleep in short naps lasting 2 to 4 hours. For the first few days your baby may be very tired from being born and sleep more than average. Therefore, to be sure he is getting enough to eat, wake him every 2 to 4 hours for feedings. Your baby should be fully awake when you feed him. If you think your baby is sleeping so much he isn’t eating enough or you have a hard time waking him for feeding, talk to your doctor.
I hope this answers your query well
Wishing you and your family good health