I think they ought to work well as a thermal store. According to
heatingtrends.com they are filled with Diathermal oil. I'm not quite sure what that is, however they state:
Diathermal oil, unlike water, has excellent thermal stability. It never reaches the boiling point, does not evaporate, and therefore does not expand so much and does not create critical pressure inside the radiator housing.
As long as the radiators do not appear damaged, they ought to be reasonably safe. The oil has a boiling point of about 300 degrees Celsius, but a pretty low rate of thermal expansion so the radiator doesn't get stressed. You might want to check what sort of temperature you do see next to the stove just in case.....