What I am counting on here is the ambient temp, see according to my understanding of these BTU ratings, it's the amount of heat that can be removed per hour, which means if we were to picture a scenario as follows:
A miner using 3kw would generate 10,236 BTU per hour, so if we use a 10,236 BTU those BTUs coming from the miner will be kicked outside and the room temp will be identical to the outside temp.
Based on that (assuming it's correct) if the outside temp in the above example was 15c, then I would need less cooling, simply put, I don't need the mining room to be at 15c, I am okay with 30c, which means probably using half the 10,236 cooling BTU will be enough to keep the room at 30c while the outside temp is 15c.
Hmm, I'm a bit curious about this one since checking the manual on our farm (not mining, true farm oink oink) HVAC the rating in BTU stands on the amount of heat it can move from the inside to the outside.
So a perfect 1 000 BTU unit will be able to move out 1 000 BTU at 10C or 40C, but in your case if you produce 10,236 units of energy those have to be removed be it 10C or 40C outside, you need the exact same amount of heat to be taken out, what will change if the outside is 10C instead of 30C is the efficiency and consumption of the unit, again, this is if we talk about a sealed room that won't lose that much heat through the walls.
I might be mistaken on this but using only half of it will end up with the room temperature going up and up till it reaches the miner's exhaust levels since you have more energy being produced inside the room than you have taken out of it!
I spoke to a guy who ran 3*S9s in a 4m*4m*3m room using only 12,000 BTU AC, so 14k BTU of heat vs 12k BTU of cooling and he said the miners were running pretty cool during all seasons of where he had them (10c winter to 40c summer)
14k BTU in 48mc2 versus 600 in 180mc2 the ratio is all over the place.
And the most important thing is that if the outside is colder even by a few degrees the room will lose heat, so if this guy had a wall in the shade with 5 degrees below and you're exposed on all sides it will be even worse.
My take would be to start with half of it and see how it works out, you wouldn't be wasting money on equipment you won't be able to sue such as the miners or you won't overspend on air units and installments you won't be needed.
Oh, and reading about the sound, just went outside, 32C right now, our office units are Fujitsu whatsoever, and my phone screams 69DB next to one of the outside units, (we have them in the parking space, cause...well, management!) so you might want to check one of those live before buying it if the sound is a concern.