I agree with Glenn, most buns do fine without anything, especially boy buns. A neuter of a young healthy boy is a minimally invasive and quick procedure.
That said, I did ask my (rabbit savvy) vet before I had my girl bun neutered last October. She said a suit is a lot better than a cone. Rabbits hate cones, and if you have to use one, it’s better to make one yourself of a small paper plate than use the commercially available plastic cones. As for temperature, a newly spayed bun is prone to hypothermia (too low body temperature) rather than hyperthermia (too high temp), so a suit could actually help in that respect.
I ended up not having to use anything for my bun. She was on pain meds for 5 days, but that’s because a spay is a lot more invasive than a neuter. For a boy you normally don’t get any pain meds to be given at home, the bun gets a long-ish lasting painkiller at the clinic, and that should be enough.
A male rabbit can technically be neutered as soon as his testicles drop, but vets often have a weight threshold they want the bun to reach.