Hi shellylh,
Probably not because cotton is very breathable and does a good job or wicking moisture as well. There is more about all the many variables that can affect sleeping temperature in post #2 here.
Wool is also a very breathable material and also stores moisture inside the fiber itself so it’s very resistant to mold and mildew and this isn’t something that I would have any concern about with a mattress protector that has quilted wool covered with cotton.
Hopefully you didn’t ruin the protector by putting it in a hot dryer for a couple of hours (they recommend a medium dryer setting).
The previous post I linked includes my comments about using a puddle pad with either a sheet or a cotton protector on top of it. While it’s not waterproof it would be water resistant and it would certainly be “good enough” for most people.
It would depend on the specifics of the blanket but a wool blanket is normally woven rather than needle punched or felted to densify it so it wouldn’t be as water resistant and it also may feel a little more prickly and not as soft as a protector or puddle pad so if you decide to go in this direction then it may be a good idea to felt the blanket.
Phoenix