If your domicile is air conditioned, then my answer is "no". What's cool & comfortable for us is still chilly to them.
Now, if you're in a warm environment & survive the summer months with a fan---then they WILL get a bit warm. HOWEVER, switching to cotton material is DANGEROUS and precautions MUST BE TAKEN to avoid disaster! There can be NO "raw edges" ANYWHERE on the material used....these little monkeys can fray any woven material quicker than you can say "fly" which could result in feet, tails, or necks getting caught in the frayed material......enough of that, you get the idea!
A suggestion would be to use cotton (outside) & lightweight flannel (inside) for pouches
. Sew each like a regular pouch,turn one inside out so the hems are facing each other, then roll the tops down & stitch them intact. (if you need more detailed instructions, send me a PM)
An alternative idea would be to use a lighter weight fleece & do a "stitchless" pouch.
Good luck to you....my suggies will be going thru the summer months with NO air either!