A year or so ago we had a thread about someone wanting to combify their cab by adding a small class D amp inside with only the front ventless panel on the outside.
I was surprised to learn that the lack of any ventilation would not bother the amp as surface conduction of the cabinet would cool the airspace plenty to avoid thermal runaway, barely warming the inside as it turned out.
So next room isolation would not be necessary, just put it in a cardboard box to muffle the fan noise.