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.

Here’s an option for fantastic quality and fit but with a cord for under $100.

Here’s a pair that’s Bluetooth and under $100 but the ear cups can run small and it doesn’t breathe very well.

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.