I don't think there is really a durability issue between "cotton" and "muslin", but muslin comes in various weights from very light to pretty heavy. I'd want to actually touch it myself before deciding, but I'd expect to be happy with a Moda product. I rather like the untreated look of unbleached muslin with the little flecks sometimes in it, other people happily use bleached muslin as white in their tops.
I typically use Kona solids, especially when ordering on line because I know what to expect. With my own projects I was using an off-white that was basically a muslin color.
Don't know about the relative coolness, but for a long time muslin was one of the only extra wide fabrics and used for quilt backing. That could be a rather thick thread but loose weave more like sheets, again -- I'd want to feel it in person first before committing myself.
I'm so glad those homespuns found a project with you. People have to be careful about mentioning wanting fabric sometimes... I'm lurking and have some designated things to go when the opportunity comes up!