Assume you have a reasonably well thermally insulated box of air which you want to keep warm. It has at least one heat source, and it has at least one heat sink. One of the options available to you is to attach a second volume to the first, on the bottom of it, hoping to rely on the idea that the coldest air will collect in the lower volume that you do not care about.
Example:
+---------------+
|Volume 1 | <-- at least one each of heat sink/source in here
| S |
+------------+ |
^ | |
heat | |V2| <-- Volume 2 added hoping to keep Volume 1 warmer
source(S)| | |
+--+
How do we figure out what affect adding the second volume will have on the temperature of the first, upper volume?
For context, this question was actually raised initially from the topic of winter camping in cold areas. Someone had heard of advise to dig a hole straight down through the snow in the bottom of your igloo to give cold air a lower place to go that won't bother you, keeping the rest of the igloo slightly warmer. We are skeptical, but we are hoping to approach this logically instead of just dismissing the idea. We want to figure out how to estimate the effect that such a hole would really have.
So the heat source is human bodies resting on the floor of the upper volume, and the heat loss is due to various things including draft from door and ventilation holes and from loss through insulation (not very significant I don't think, as the snow actually insulates surprisingly well).