Here's an examples of adding cob to wood stoves
https://www.google.com/amp/s/shephersglenfarmblog.wordpress.com/2014/11/08/cobbing-a-wood-stove/amp/
No word on the long term outcome.
Maybe cob directly on the stove is a bad idea.
There are many posts on Permies about adding mass to woodstoves, most recommend stones, pavers, bricks and concrete blocks around and over the the stove but not touching it.
Some suggest water in barrels or pots.
I'm keen on using the tanks from water heaters to store water in, they actually look pretty nice cleaned up, a dark smooth steel.