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Russ noted that someone is using thermography to study thermoregulation in elephants:

Wits University has just completed studies on how elephants cope with high African temperatures and how that influences their behaviour. In African savannahs, elephants are exposed to high environmental heat loads during the day and low ambient temperatures at night and yet these animals are able to cope quite adequately.

Animals that run the risk of losing energy by dissipating heat often deal with this via regional heterothermy, i.e., wading birds have cold legs so there is less of a heat loss when they are standing in cold water. This is often accomplished by using counter-current setup which I explained in detail before. Elephants have the opposite problem - overheating and they solve it by heating the periphery (e.g., ears) and letting the heat dissipate. They also deal with walking on hot ground by heating their feet, it appears.

Or, if you'd rather look at basic principles than biological details, you may just start by assuming an elephant as a sphere. Bigger the sphere, smaller the surface-to-volume ratio and harder it is to lose heat. That is why penguins in the Antarctica are bigger than penguins living further north on the coasts of Africa or New Zealand (this is also called Bergman's rule in ecology).

Also, deviating from the shape of the sphere increases heat loss. That is why desert foxes have longer ears, snouts and tails than Arctic foxes (this is called Allen's rule in ecology).

Since the elephants at the NC Zoo are about to get a new house with a pool, perhaps this can be a good place to study elephant thermoregulation as well.