Here's what we know:
* Indirect evidence: Scientists use seismic data (from moonquakes) and gravitational measurements to infer the Moon's internal structure and temperature.
* Models: Computer models help us simulate the Moon's formation and evolution, which allows us to predict the core's temperature.
* Comparison to Earth: Comparing the Moon's size, composition, and geological activity to Earth gives us some clues about its core temperature.
While the exact temperature remains uncertain, these methods give us a good idea of the Moon's core being considerably hotter than its surface, but much cooler than Earth's core.