baby temperature

Jalayna
So my bf is so concerned about the baby being cold because the outside temperature at night drops down to about 46 but but during the day it's 73. He puts the heater on to where it's about 81 in the house. When I go to breastfeed my baby we both start sweating and I feel like my baby is getting uncomfortable. Even when I go to take him out of his bassinet it's like he's in a pool of his sweat. My bf starts fighting with me saying he needs to be warm and not cold but I feel like our baby is going to overheat and I'm worried about SIDS. What should I do? And what should I tell my bf to tell him it's okay to turn the heat of? 
UPDATE: last night I picked the baby up from the crib and he was drenched in sweat. I ran out to my bf and yelled "you think the baby still isn't hot?!" He looked scared and said ok turn the ac down. He's starting to realize he isn't always right