When it was really hot over the summer I got two of the cool pillows from Wilkos, they are a gel sheet and I found them quite good for cooling down initially. They don't need to be kept in a fridge but are a lot cooler if so. Think they were about £9.99 each.
Ah, this one:
https://www.wilko.com/en-uk/jml-chillmax-pillow/p/0460656
I only use a duvet when it's really cold. I use bedspreads usually in a nice cool cotton material. Sleep on top of the duvet with the bedspread (and usually a blanket on the side in case I get chilly). Nice and lightweight to shift around overnight too, depending on how warm you are.
Good to get things generally in nice cool cotton rather than more synthetic materials.
You can get light cosy socks from places like Primark, warmer than normal socks and pretty cheap. They always have lots for women so would be surprised if they didn't have ones for children too.