My 4B-ST runs Hot

My 4B-ST runs warm, but not hot to the point it's uncomfortable to keep your hand on the lid -- even when driven hard. Is your amp getting sufficient ventilation? If it's in a cabinet or has less than 3-4 inches on all sides, you may need to provide it more space, or install a small fan (there are some very quiet types made for audio installations).

You mentioned that the amp seemed hotter on the right side of the top. The 4B-ST is a symmetrical construction, with the heat sink modules each containing a separate channel of amplification, with the twin toroid amps occupying the center of the chassis. The only other factor I can think of that might cause excessive heat on one side (given the symmetrical internal layout) is a badly adjusted DC offset. I think your problem merits a call to Bryston, since excessive heat will decrease the life of the solid state parts and output transistors.