I feel eaves are more to keep the drip line from rain from hitting the foundation than for any heat abatement. Typical spanish style roof will not have anything on the side that isn't sloping for example. Just sort of ends flush with the wall. Some don't have any eaves at all really.

Strange then then places with lots of rain and wind (Ireland, Netherlands come to mind) hate eaves. I guess it keeps builders in business.

Ironically when I had a 200 year old thatched cottage it had 'eaves' by virtue of the thatch extending almost a meter from the wall. It had built up slowly over centuries of rethatching.

My experience is mostly with Californian houses that definitely had eaves.