It is obviously very onerous to generate heat at all, although it has advantages. We don't have to lie on the sun like a crocodile to get warmer. And we avoid the freezing of our body water by out own means. But wouldn't just a little of heat be enough?
Why do humans go as far as 37 C? Couldn't we just have a temperature of 10 C to avoid freezing but stay at it?
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 (< 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.
If I had to guess, the reason human have the body temperature we do is because the ancestors of placental mammals had that body temperature. You will notice that all placental mammals have nearly the same body temperature http://www.infonet-biovision.org/AnimalHealth/Tools-livestock-care-and-treatment
That being said, birds have a higher body temperature than placental mammals http://www.sciencedirect.com/science/article/pii/030096299190122S
But why the higher body temperature....as you say why not just high enough for muscular activity?
One potential answer is at higher temperature, animals are better able to resist fungal infections for the simple reason that most species of fungus don't grow well at temperature above room temp. Declining by 6% of species for every 1C rise https://www.sciencedaily.com/releases/2010/12/101222121610.htm. The optimum as calculated in terms of energy cost to maintain that high body temp vs number of fungal species to fight against was estimated to be 36.7 C, about body temp for mammals, and resting body temp for birds.
