Hi Jodi,
Thanks for bringing up the idea of wood benches. Yes, you can use a wooden box to surround and control the masonry thermal mass 'infill', as long as you use good clearances to the hotter parts of the system (the firebox, upper barrel, and first few feet of exhaust). Our bench at home has wood trim on the bench and bench top, and you can see we are very comfortable with cushions and even books right in contact with the bench mass. But I chickened out and used a similar-colored Saltillo tile for the mantle behind the barrel.
Paul Wheaton's 'Portable' Rocket Mass Heater also used a wooden box, and we've advised another client on a proiect that involved a much larger wood-and-infill design that's working well.
Monitor the temperatures for the inside surfaces of the wood -you want to be sure it stays below about 150 F / 65 C to prevent long-term baking and flammability hazards. Ours runs maybe 90 F surface temps for the hottest parts of the bench, most nights. But around the firebox it gets up closer to 150.
When we did a variation on the portable heater for last year's Missoula workshop (the one on Paul's DVD set that's coming out soon), we added extra insulation around this area and heat shielding behind the barrel.
Yours,
Erica