I have 4 of these in rotation. I wear one every ride, regardless of temp. They do not make my head hotter and keep the helmet pads clean. I actually have some old Performance brand caps just like these, but I don't think they sell them any more. The ones I use just cover the top of the head, stopping well above the ears. Very minimal.
https://www.performancebike.com/pace...9-9910/p540820
I also have a couple Headsweats do-rag type things. Functionally very similar, but cover right down to the tops of the ears, and they have that stupid faux tied/knotted looking tail in the back like you'd have with a bandana do-rag. I prefer the simple/minimal helmet liner.
I've been looking for something similar with a drape in the back big enough to keep the sun off the back of my neck, but haven't found anything that looks right yet.