Have you considered bone conducting headphones? Since they don't actually cover your ears you stay cool, and if you want to block out outside noise they come with ear plugs.
I wear mine constantly.
I couldn’t recommend these more! The quality of the sound is top and they’re fucking awesome. Never worry about sweat making my ears slippery or anything. Also the first time you use them it’s kind of a strange experience.
Over the ear that stays cool sounds like a request for open back headphones. But it's difficult to find anything wireless with large breathable earcups for under $100.
It's difficult to find something so specific with the limiting search criteria. If you open up the budget or remove another requirement such as over ear then the search becomes manageable.
I prefer Bluetooth, and would really like to see something that will not allow low security encryption hacking in the initial arbitration, but I know stuff like this level of technical rarely makes it into public documentation.
I'm using Soundcore Q30, about 80€, ANC, BT, and if you want better sound, there's AUX too. I use them for work too, so several hours without taking them off, and I'm still in love with them.
I've used some "Ausdom" headphones for somewhere between 2-3 years. I think the branding is just a random name generated by whomever paid for a production run at a decent quality Chinese factory. They have Bluetooth with an audio jack bypass, and active noise canceling. The ear covers seem about average ovals. I just have a big head and they barely press against the upper back edge of my earlobes. They are decent quality. The leather like vinyl is nice but just gets a bit warm for extended use. I think I paid $30-$35 on either Amazon or eBay. I would just get some better covers if I could find something compatible. The headphones aren't bad but the vinyl on the ear covers has started falling apart from use.
I wear 3m work tunes with gel cushions while working outside year round. They are generally under $70 and I don't notice any significant hest issues around my ears, and that's even when it's 100 degrees outside.