It is general practice to put a bucket of water on top of a wood stove to keep air humidity under control during the burning of the stove.
But, such a bucket is also bound to keep some more thermal energy captured for a longer time (i.e. absorbed via the metal frame and released into the room in a more smeared-out time-interval). Does it make sense to boost such thermal "dead weight" for typical operations and given typical "family-house" stove products currently for sale on the market?
(Besides putting a larger water bucket on the stove, one can also add material to exposed sections of the chimney. Isn't putting heat-exchangers around chimneys common practice?)