Originally Posted by Oukile
I'm not quite sure that body temperature itself is the issue, since small mammals can live in cold regions and small aquatic birds do very well. On the other hand, a small animal would have a relatively higher need of oxygen (because of higher metabolism and probably relatively higher energy expense for swimming). With less body mass to store oxygen, that would make a lower ability to dive.
Retaining body heat in air is a lot easier than it is in water, because water has much higher thermal mass than air. Hair and fur insulate by trapping air against the body and cutting down on heat loss by convection. As someone pointed out above, hairy (and feathery) animals in the water keep warm by keeping a "bubble" of air trapped around their bodies. But these animals have to spend a lot of time at the surface preening. The alternative to hair/fur is blubber insulation. But a layer of blubber makes the animal bigger.
Most sea creatures, large and small, are cold blooded. The warm blooded ones, whales, dugongs, tuna, great-whites, etc., are mostly large bodied. I doubt a mammal the size of a mouse could spend a majority of its time in the water and still retain its warm-bloodedness. It could adapt by evolving a tolerance for a low core body temperature while in the water (and maybe warming back up at the surface).