Please dont put hats on your babies when they are sleeping. its the only way they can regulate their temperature if they overheat.
Best to leave little bald heads alone!

As for the warmth factor - everytime I put socks on jenna inside her sleeping bag, she doesn't sleep through. We have her in long sleeve top, flannel jammies, sleeping bag (2.5TOG) and I've started putting a light cellular blanket over the top. She never has cold feet when she wakes up - so I dont know why I put socks on her?

We've always gone on the side of caution with heat - I keep her colder rather than warmer, and I try to use natural materials in her bedding - wool and cotton preferably. I hate the idea of polarfleece in her bedding - I wouldn't want to sleep in it, so I wont make her.