Moon May Be Geologically Active
dptalia writes, "For decades scientist have thought that the moon has been 'dead' for about 1 to 3 billion years. However, new research points to the idea that the moon may have been volcanically active as recently as 1 million years ago. In fact, NASA geophysicist Paul Lowman believes the moon's core is still molten."
I'm not sure what you mean by 'ambient temperature of space', because temperature is a property of matter, and space is kinda empty, so there's nothing to compare it to, unless you want to call it absolute zero, in which case the moon will be quite a bit hotter than that no matter what.
The next nearest approach I would think would be to figure roughly what temp. an otherwise 'dead' object of the moon's size would reach just through the ambient radiation in space, plus collisions (probably insignificant, but maybe not), etc. This has to be tougher than it seems at first glance, though, or I would expect they would have already figured it out.
Unpleasantries.