space - Can an asteroid have a molten core?

Yeah, entirely possible.

There are a couple of examples of asteroids that we've identified which may have, or recently had, molten cores. 21 Lutetia is a notable example. Vesta is another.

The main issue is that because of their size, the ratio of surface area to volume is higher than the average planet. This means it cools much faster. So while some may have molten cores, they won't stay that way for as long as a planet might. Additionally, most aren't very near large gravity wells like a moon might be, so they don't have the same tidal forces adding energy to their interiors.

All this makes it less likely to find an asteroid with a molten core, but it's not impossible.