Are you in the UK? All formula here should say to be make with water that's roughly about 70C (so that's boiled in a kettle and left to sit for a few minutes, up to 30 minutes). I know the two brands I've used have. But it's different in other places. For instance in the U.S., they don't always say to boil water and even say to use bottled water (which we don't here because of the high salt/mineral content). But there's also liquid concentrate in the U.S., which maybe is packaged sterile? I'm not sure. If you're in the UK, yes, it should say to use boiled hot water.
As for rapidly cooling, yes, it's just putting it in a bowl of cold water to cool. You might need to refresh the cold water once or twice depending on your room temp. I've found that on really hot days (which we've had recently), the room is so warm that things don't cool down as quickly, so I have to change the water to get the bottle to cool faster. Adding ice if you have it to hand also helps.
