I think that it would feel like it was at body temperature (whatever your body temperature is), for the same reason that it’s perfectly reflective. Just as it reflects light (because it must, because it can’t absorb or transmit it), it would also reflect heat.
If I were designing the concept from scratch, I would probably say that the shape of a stasis field must be convex, and that trying to put any other shape in a stasis field would give you the convex hull of that object. That’d severely limit (though not entirely eliminate) the structural capabilities of a stasis field, especially when you consider that they’re also frictionless. But that doesn’t fit with the stories as written, because then, for instance, the Sea Statue wouldn’t be recognizable as a “statue”.