Hat with mosquito netting on top

She should consider just cutting ventilation holes on the top of the hat. I know a few people who do that.

Based on someone's elses recommendations here; I recently picked up a Henschel Breezer.

I like it a lot. Certainly cooler than my old Tilley.

There's several styles and vendors available; but here's one on Amazon:

I've bought far too many hats, half of which I threw away because hat designers are *really bad at designing hats* and do stupid things like putting two little holes in the side instead of replacing the entire crown with mosquito net.

My favourite hot weather headgear is a Sunday Afternoons Aero Visor for shade…
http://www.sundayafternoons.com/aero-visor.html
… worn over a microfibre buff to wick/evapourate sweat and add a bit of UV block (I'm short of hair).

One could perhaps wear the visor with (part of) a mosquito headnet, if an all-around brim is not required.

So I know you can't really tell in these photos, (http://www.kavu.com/Product/175-20-/Chillba-Black.aspx), but the Kavu Chillba has an all-mesh, headfitting, adjustable sweat-banded skull-cappy thing underneath the brim. It holds the hat to your head quite securely (and if not secure enough, has a chin strap), but still allows for the most amazing flow of air all around your head, because the actually hat part only rests lightly on the top of your head. (If this is too obscure of a description, I can try to take photos of it for illustrative purposes.) It keeps the sun off of the tender head and face, but isn't great for neck protection. I combine it with a Sea To Summit bug net, (http://www.seatosummit.com/products/display/9), for awesome sun & bug protection with great ventilation. The combo weights 5.2 oz/149g. It offers reasonably good protection from rainfall, though it's not waterproof or even water resistant, so it soaks up quite a bit of moisture and becomes heavy. The brim is also not big enough to constantly bang on the top of my bag in the back, which is a big plus. Just my $.02!

David,

Bingo. I think the Henschel-Breezer (or something very close to it) is the hat we recently saw.

Thanks

Sunday afternoons has a few hats with partial mesh on the sides (Adventure, Sport, Offshore). I wear the Sport which is 2.2oz. If that's not enough ventilation, check out the visors that wrap almost 360 degrees (Sicily, Garden) and have an open top. They list the Sicily at 3.2 oz.

Columbia's Coolhead cooling brimmed booney hat has a large area of mesh. The cooling action of the fabric works okay. (better than nothing)