I think putting them in the fridge for one to two days is the most common. I asked the bottling after pulling it out of the fridge question and I was told that it's fine to pull it out of the fridge and bottle it with the priming sugar. Once the bottle temps get to room temp, the yeast is happy and can start carbonating the bottles.
For testing carbonation, fill the first and last of the batch in two 16 oz bottles like you were describing, and when they are hard like when you first bought it then stove pasteurize all the bottles.
And yes, they need to be left out at room temp to carb up. The time this takes is between three and 24ish hours. So you need to have a free weekend when you get to the carbonating and pasteurizing because it's a guessing game for how long they will take to be ready.
Thanks for the information on this process. I made some great cider and then cold crashed it at about 1.00 two days ago. I added some honey to make it a bit sweeter, and planned to keep it in the fridge until it was consumed.
The only problem is that I made it a bit too sweet. So I'm going to bring it back to room temp. and let the yeast start up a bit until it dries out a bit. Once it does, I'll follow your instructions.