[INTPenis]

Maybe it wasn't finished? And the ones out of stone could be a poor persons attempt, because stone also retains heat.

I actually like any theory related to heat because that's what the map indicates. Any other theory is related to things and actions that were common throughout the empire.

[arp242]

Maybe. I tried to find a catalogue of dodecahedrons, but I couldn't really find any in a few minutes of searching, so I'm not sure if all except one doesn't have any holes, or if there are more of them. Many of the images seem to be of the same few objects.

As for heat: how did people heat their homes? Rich people had their fancy underfloor heating, but what did poor and middle-class people use? In Celtic and medieval times they would typically use a hearth (i.e. fire) – it seems to me a candle just doesn't give enough heat, and you're going to need a hearth anyway for cooking. I would imagine that's also what they used during Roman times since that's what's used both before and after the Roman era.