Times up!!!
Alright you passel of miserable lubbers, open up yer lug-holes and listen up!!!!
The question asked was ‘what is a Brass Monkey, and why is it necessarily made of brass?' Note, I didn't ask fer no fairy tales or repetitions of circular reporting pulled off the internet neither!
A Brass Monkey is a triangular rack, made of brass and bolted to the deck between the guns of any FRENCH-BUILT sailing warship built after about 1750. It is used to stow ‘ready-use' cannonballs in a flat rack, NOT ‘stacked up like a pyramid,' as even a lubberly Frenchman wouldn't be so stupid as to do such a foolish thing on a ship (the first time the ship heaved over from a swell or wave, the balls would be all over the place if they were stacked up!!), though soldiers in a fort might consider it. It is very similar to a rack used in Billiards or Pool. If you referred to Boudriot's books, he shows Brass Monkeys CLEARLY located on the decks of French-built frigates in both his scale drawings, and in his photographs of contemporary ship models, and in neither case are any of the balls stacked up in a pyramid.
A Brass Monkey is made of brass, because when cast-iron cannonballs are left lying around for any amount of time in a marine environment, they will RUST, and quickly too. If the Monkey was made of iron, the balls would rust onto the rack, making them very difficult, if not impossible to remove without some sort of tool. If the Monkey was made of wood, the constant shifting of the ship and the cannonballs would soon wear down the Monkey, making the balls loose and liable to fall out in difficult weather. THIS is why a Brass Monkey is necessarily made of Brass!
Many of you mentioned that British warships used either shot racks or shot ‘Garlands' to stow cannonballs, and largely, that is true. However, it is ONLY true of British-built warships, and does not include the (many!) warships captured from the French (British builders were too cheap to use brass, which is a situation largely still true today, but were happy to use them if they were already aboard!).
Shot garlands are usually found on the upper decks of British-built warships, and consists of a small wooden shelf bolted onto the bulwark with cups to hold a few cannonballs. A shot rack is found on the LOWER decks of British-built warships, and consists of a slightly raised straight wooden plank running fore and aft with cup holes to hold cannonballs and is bolted to the deck, located BEHIND the guns near the centerline of the deck.
The Brass Monkey is superior to either the shot garland, or the shot rack, because you can place more cannonballs in a Brass Monkey than either the garland or shot rack, and of course, the balls are located near the muzzle of the gun when it is withdrawn thus being more accessible for reloads. What does this mean? It means you don't need as many otherwise useless lubbers to sweat and labor up and down companionways lugging cannonballs up from the shot locker, and instead can just use Powder Monkeys (generally small boys) to bring charges to the guns.
As to the old saying ‘Cold enough to freeze the balls off a brass monkey,' that was NOT any part of the question, or its answer. As far as I know, it is far more likely that the original expression was ‘Cold enough to freeze the balls ON a brass monkey' (i.e. the balls were literally frozen into the rack, either through ice, or possible contraction of the Brass Monkey itself), which was subsequently and repeatedly misquoted by ignorant landlubbers at a much later date, such as yourselves. No pyramid of cannonballs, no balls popping out, just stuck in place and therefore useless, much as yourselves! All of you up to the masthead, don't come down 'til you ain't ugly no more, and don't fergit to bring that miserable French 'banana hammock' salesman with ye (Shannonman!)!!!!