Wow I'm surprised at how many people had the baby actually removed from the room. I was not physically seperated (in another room) from my son at all during my hospital stay. He was placed on my stomach immediately, wiped down on my stomach, then placed on my chest (his cord was super long). When I was ready, I handed him to my husband who oversaw the APGAR and weight/length in the same room while I was being stitched up. The pediatrician check, hearing test, PKU test, etc were all done in my room. The only time they offered to take the baby from my room was for a bath, and we refused that.
Its so important to have the baby with either you or your partner. There is usually no need for heat lamps, etc. Skin to skin contact with Mama is ideal. I remember the first night, my son was in his diaper, I had no top on. I put him chest to chest with me, covered us both with a blanket, and we slept for 5 hours!!! It was awesome. Actually he slept, I stared at him.
But every hospital is different, find out their restrictions. And write that birth plan!! Remember, the vitamin K and the eye medication can wait!!! That eye goop really blurs their vision. Don't let that interfere with the bonding. We waited about 2 hours I think.