I've played around with doing just that but have found it to be ineffective. The thermal mass bench doesn't really get hot
enough to warm fast moving air passing by, over, or even inside the bench. I.e. think of the bench being around 90 degrees F, and the fast moving fan driven air temperature being in the range of 50 to 60 degrees. That fast moving cool air will not be heated to anywhere near the 90 degree temperature of the bench. Hypothetically, if the fan driven air managed to warm to say 80 degrees, even an 80 degree "breeze" in the house will be felt as being cooling to most folks.
However, when being fired, the RMH barrel gets "
wood stove" hot and can easily heat fan driven air.