I forgot to add that we heat up a wheat bag and put it in DD's cot while she's having a feed and then I take it out before I put her back down. It's really nice and warm and she snuggles in and falls asleep well. Some nights I think 'oh she'll be fine, she won't need it' and boy am I wrong and it takes ages to re-settle her. So, not sure about where you both live and how warm/cold it gets but it makes sense - why go from warm and snuggly cuddles with mum to a cold bed?
Also, you can try putting one of your pre-worn tops into the cot - tuck it in like a sheet that they sleep on and it smells like you. We did this in hospital and for the first week at home and she seemed to settle better when we put her down for sleeps.

I remember before deciding to try for a third, thinking 'do I really want to go down this path again' and it wasn't the whole pregnancy/birth stuff, but the hard yards that comes after the baby is born, the silly dieting, feeding, feeding, feeding, trying to settle an irate baby....... it's sooooo much hard work! But worth it all the same.
Hang in there, hopefully they'll throw you a better night's sleep soon