Ah nights haven't been too bad since we discovered that Lucy loves her pram, and we've also swaddled her. Not swaddled too tight but enough that she feels secure.
So now she feeds every 3-4 hours and has started telling us when she is hungry (before we were waking her to feed and that unsettled her lots). And in between feeds she sleeps in her pram.
I usually wait till she's fast asleep before I put her in her pram but if she wakes up again I often just have to push it for a few minutes and she's fast asleep again.
I don't think babies learn to self-settle till they are older so its ok to put them down after they're asleep at this stage.
We have had a few crazy evenings though where she cries and cries. We avoided that last night by doing everything around going to bed differently and that worked. So instead of being on a 3, 6, 9 timing we're now on 7.30, 10.30, 1.30... Feels more civilised at the moment!
The coldness of the bed could be waking Amelia up so you could warm it first with a hot water bottle. Or if she need your smell to sleep you could use a blanket that smells of you.