Under conditions of hypoxia lasting more than about two to three hours, the concentration of 2,3-DPG increases substantially. It binds to haemoglobin, facilitating the release of its oxygen molecules. The effect of this is that at any given partial pressure of oxygen, more oxygen is released than would otherwise have been, and so increased 2,3-DPG levels mean that the tissues get more oxygen. Since this was all a response to hypoxia in the first place, order is thereby restored to your body.
There are three other factors that also increase oxygen dissociation from haemoglobin, namely a decreased pH, increased carbon dioxide concentration, and increased temperature. The first two of these also make sense: hypoxia causes lactate generation and thus a decreased pH, and poor blood flow to an area causes carbon dioxide to build up. In either case, the implication is that the tissues aren't getting enough oxygen, and so more oxygen is duly deposited there. I'm not sure about the last one, though. Perhaps, instead of being an 'adaptation', it's simply an unavoidable effect of changing the temperature. (Many molecules, like enzymes, are quite specific as to what temperature they prefer; even a 1 or 2 degree Celsius difference can deform or destroy them.) Thoughts?
P.S. Unhelpfully, increasing the amount of oxygen that haemoglobin gives up for at any particular partial pressure is sometimes known as 'shifting the curve to the right', since this is what the new oxygen-haemoglobin curve would look like, when compared to the first one.