Mike G wrote:I stick mine in my biggest stockpot, make the brine around it, stick the whole thing on the bottom shelf of the "beer" fridge (before I had one, I was known to simply set it outside, weather permitting) and it all works great.
If I don't have room in the fridge, I stick the brining container in a picnic cooler. The last time I had a turkey too big for the pot that fits in the cooler and no room in the fridge, I improvised with an oven-roasting bag (about $3 per box of 5) inside a trash bag, as mentioned upthread. I poured the brine around the bird, closed the whole thing with a twist-tie and then added ice and water to the cooler around the outside of the bag so the whole thing was submerged. It worked great.
The other thing you can do if you can't refrigerate is to put the turkey in the brine in the pot or a smallish cooler and add sealed bags of ice.