I used to toy with the idea of building a hardhat fan, but eventually rejected it. There's a lot of reasons it would be a hassle, but the humid climate here would make any benefit marginal, and not worth the hassle cost. In a drier environment, maybe.
Cowboy hardhats look awful. I've worn full brim regular hats, and they kind of suck. They're probably marginally better now due to lighter materials, but still. A cowboy hat amplifies all the drawbacks. AFAIC, they're made for looks, not real use. I've been pretty happy with my Vertex Vent as a construction helmet, as well as for all my saw related stuff. The big vents let in a bit of a breeze, and exhaust heat. Not perfect, especially with humidity, but it's light, and pretty comfortable. I knot corners of a bandanna and slip them down between the muffs and the helmet for neck sun protection. A poly headband on your head does more than you might expect to keep sweat from dripping in your eyes.
It's very hot and dry here. Well, august gets humid...and I don't do tree work when it's crazy hot. Something to extend work time would be nice. Sometimes at work (machine and weld shop) we do have to work out in the heat. I had a regular hard hat on the other day and it was significantly worse.
They make helmet donuts. I usually see them on flaggers where they're pretty much just standing on the road all day. There's at least one guy at my client's company that wears one working. Wide brim, and they look very light, but I've never worn one. Unsuitable for treework I think, unless you were just falling timber. Close contact with limbs and brush would make it a hassle.
A bit of cold water poured over your head works wonders cooling off. I've got enough hair that will hold it for a bit so it can do its job, but lacking that you can soak a hat or bandana to do the same. It's liquid humid here usually so stuff just doesn't evaporate, so much so that welding gloves and stuff are dried using the radiator exhaust to heat them up enough to dry out. The only way I've found to really do the heat and humidity in this setting is by physically drinking (chugging) as much water as possible (with electrolytes and salt as needed to control cramping), and then dumping water on you to cool off if needed.
Going to sit in a truck with the ac blasting during frequent breaks can do wonders too, 20 min of relaxing, eating and drinking, and soaking up ac every couple hours makes you a new man. I've looked into a cool vest pretty hard, but with me working as a fitter where I'm welding all day i just can't see it lasting or even working in some spots (the ones i always seem to find myself in). I've got a few yeti style water bottles, and I'll fill them up so i got plenty of water with me at all times. It's cool, not cold, if it's too cold you don't drink enough. Some ice cold water is handy to quickly drop temps tho, welding pipeline it was part of the contract that you got ice and bottled water daily for your rig, so i always made sure everyone around me had water. You can always let it warm up a bit if it's too cold.
Welding in the desert where you're at must be hell, but maybe the dry heat part might work to your advantage. Evaporation happens there quite quickly, so your sweat actually does its job. I would likely be in long sleeves to wick water, and would likely be tempted to dump water on my clothes there to evaporate before the sweat, maximizing cooling. Here you would just stay wet all day if you did that, which isn't the end of the world because you'll be drenched anyways from all the sweat that just sits there.
A weld cap or bandanna under the hard hat adds another layer that can evaporate water to cool you off, so that's what i would be headed towards. Every so often stop to drink water, splash a little bit on your head/clothes, and carry on. Crude, but effective, and i haven't found anything better yet myself. I would also be looking into making a redneck swamp cooler fan thing, think 5 gallon bucket, fish tank pump, burlap bag, and a big fan. Definitely a canopy or umbrella too.
Ditto on the soak your hair strategy. Soak till it drips and wets your shirt. Takes about an hr to need a top up.
I used to do this when I played field hockey too. Being the goalie all togged up in full helmet and body padding, only way to moderate my temperature during a game.
I'm also a fan of a neck flap for sun protection
During my entire tree cutting career I only had one helmet, a Petzl. It was ok but I still hated it. Recently I have been working with a crew where everybody wears helmets when aerial work/cutting is going on. The boss never said a word to me, but I bought a Protos out of respect and to better fit in with the crew. As helmets go, it's not bad at all. Light, well ventilated and comfortable. The built in shield and low profile earmuffs are sweet.
I love the protos. Stay away from the tactical colors. I got the tactical black/red one and the helmet itself is a flat black with red stickers. Attracts a lot of heat. I’m half tempted to sell it and get a different color