Cold cot

[iamverytired]

I posted a couple of days ago about using a sleepyhead in the next to me cot. I haven't continued to use it but sleep has been as bad as ever - last night baby slept the first hour in his next to me, and then I had 5 attempts at putting him down before giving up and co sleeping, which I don't want to do. I really think the issue is the next to me feeling so cold, so he's waking up when I transfer him into it. I have been using a hot water bottle but when he wakes every hour it's disturbing having to boil the kettle when it goes cold. Plus it only heats a small part of the cot but the rest feels stone cold. The bedroom is between 18-20 degrees but I always feel cold at night so I imagine he does too. I used to follow the sleeping bag guidance and only have him in a sleep suit inside it but a few weeks ago he felt freezing and his temperature was 35.5 so I've added a vest ever since. So he's already wearing more than guidance suggests he should. The heating does come on in the night if downstairs drops to 18 degrees but I'm sure upstairs is warmer anyway. Any ideas for warming the cot safely or adding any more layers to stop baby feeling so cold and waking up as soon as he is put down?

Any where you can move the cot too? Is it near a window or door at the moment ?

I remember these days well and also used the hot water bottle method. Can you take a flask up with hot water in so it’s less labour intensive in the middle of the night to refill it?
How old is baby? I have to say no matter what I did my kids didn’t sleep when they were tiny. They are programmed to want mum.
We also co-slept a bit against my wishes, but I made sure it was very safe. A vest and sleep suit sounds fine but I wouldn’t add more if you’re sticking to the guidelines.
Hang in there, it does get better. Can you go to bed really early and leave your partner in charge of the baby til midnight? Then at least you get some sleep before the horrendous night shift?

The cot is next to the bed on the opposite side of the room to the window and I pulled the doors to so there shouldn't be any draughts. It is quite close to an internal and external wall in the corner where it is but I don't have any space to move it further away. The mattress/sheet just feels like a cold slab when I put him in it. I move the hot water bottle around before I put him down but I feel like it draws the warmth from his body as it's too cold to heat up much at all, so his head is temporarily warmed but his body can't stay warm in it for long. I don't have a very big flask but I could try that for at least the second time it needs changing. Baby is 14 weeks today. He's never slept more than 2-3 hours at a time but now it's every hour or less. Except for last night co-sleeping he slept for 3 hours, an hour and a half and another hour, and there was no prolonged settling inbetween, it was bliss 😂.
Sometimes my partner does have him before bedtime yes but he works and is being kept up through the night too so it's not possible every night. I had to send him to the spare room as he was as sleep deprived as me and I've resorted to giving baby to him at 5am so I can get a couple of hours!