Why humans have the temperature they have?
It's simply not possible for humans to live with an absolute body temperature below 20 C for the simple biophysical reason that it would prevent flux of protein through the Golgi and therefore biosynthetic and secretory pathways, as well as endocytosis. The lipid membranes become too "stiff" to correctly function.

My own sense is that the nominal 37 C body temperature is a result of all of the ATP hydrolysis reactions that happen all the time. The chemical reaction is not efficient, and some of that energy is absorbed, heating the tissue.

There are various grades of hypothermia, from mild (33–35 °C) to severe (&lt; 28 °C). Death from hypothermia results only from prolonged exposure, for example, being in ice-cold water results in death after 50-100 minutes. The basic mechanism is that the body dies from a combination of decreased electrical conductance of pacemaker nerves in the heart, and a slowed heart rate incompatible with sustaining life. Ultimately, hypothermic death is a dysregulation of the body's thermoregulatory mechanism, rather than an immediate biochemical problem as I've pointed out above. For a detailed review, there is an open access article detailing hypothermic etiology and pathophysiology.

M.L. Mallet. Pathophysiology of accidental hypothermia. QJM (2002) 95 (12): 775-785.