It might be a silly idea, but that's what I do with my weighted blanket when I want it to be a bit heavier: I fold it just over my shoulders, and leave it single on the rest of the body. It doesn't change the thermal properties much, but it feels better. So you could try a lighter weighted blanket (10 or 12 lbs), folded on the shoulder. The problem is that lighter weighted blankets are probably not necessarily cooler than a heavier one.

Aluminum chain mail blanket. Excellent cooling, less weight, and can be put inside a cotton or wool cover.

My cousin has one, but I don't know where they got it. I need to ask them since I have the same issues in the summer.