Not all tiny fans are loud. I built a very quiet Raspberry Pi IP camera[1] actively cooled by a little Noctua fan[2], and it's so quiet I can't hear it when I put my ear up next to it (as you'd expect from a fan that costs almost $1 per cubic centimeter).

[1]: https://github.com/milkey-mouse/basket/tree/master/hw/case [2]: https://www.amazon.com/dp/B00NEMGCIA