Building bench with heat transfer from adjacent stove

I would love to have a rocket mass heater but can’t afford to replace the 6” flue in our existing stove with the complaint options.  My stove does get pipping hot and the wall next to it gets to 175 degrees F.

I was considering building a masonry, clay, cob, or similar bench. I was thinking of using a sheet of aluminum embedded vertically and sticking out next to the wall that gets hits with the heat. (The stove is in a corner. To the left would be the bench. To the right is a door so that side isn’t an option.

The idea being the aluminum would transfer the heat to the bench sorta like a thermal mass. I’m thinking aluminum because it’s cheaper than copper.  The idea of using water or another liquid isn’t appealing because of the added complexity.

Does anyone have thoughts or suggestions?