What you need to think about is the RATE OF HEAT TRANSFER. In other words, yes- the heat will dissipate into the cold night. But how fast? A wooden or even plastic rain barrel would actually be a pretty good insulator, not desirable. Even in a metal barrel, how fast will the heat soak through and then transfer into the air? Not fast, because it's just one flat surface between the two.
If it's windy, that would help, by making the rain barrel come into contact with more air. Now, what if you add surface area to that breeze? In other words, a radiator with a fan sucking cold ambient air through it, right? Now THIS will be able to move enough heat, FAST ENOUGH, to allow for a big temperature drop in a continuous stream of hot water.
That's the worst case scenario. If you have a large stock tank, hot tub shell or some such open topped container- and importantly, if your CO² burner is only running occasionally and not constantly on- then the natural action of water evaporation and heat transfer in such a container could well suffice, especially over winter! The rate of cooling could be accelerated by doing tricks as simple as pouring the inlet water into it from a few feet high, creating a cooling waterfall, splash and circulation.