Inside you have old plumbing systems, knob and tube electric, old boilers and radiators or gravity fed furnaces.

The heat was boiler and radiators, the AC was window units. 

The boiler units landlord pays a high water bill and often also the gas bill, they typically also rent for lower prices then hvac heated units especially when it's those big radiators as in photo.

It is in a window over a cast iron radiator!

I kept the radiators just painted them white to refresh them.

I know tons of folks who refused to use microwave ovens back in the 70-ies or 80-ies because they were convinced that the radiation will poison your food and give everyone cancer.Incidentally, Government recommendations in health matters have an extremely spotty record, in my opinion.

The clay may radiate after the candles have gone out, but you're still talking about heating a room with candles, which is not a particularly great idea.

Radiators, cast iron baseboard water and even fin baseboard systems are all prone to freeze damage.Horizontal runs in the domestic hot water delivery system are also prone to freeze damage.Food in refrigerators and freezers with the electric turned off all particular smelly messes.

I suspect it is a boiler (probably with period cast iron radiators).

A hose clamp and a piece of old radiator hose.Don't make a bid deal out of it.