KDSS does not have a 'shock' (aka damper) like a normal suspension system. Don't get me wrong, the vehicle does have dampers but they are independent of the anti-sway bar (KDSS) system.
The KDSS piston(s) are either hydraulically locked or hydraulically free to move. A valve opens or closes and allows the flow of fluid into/out of the piston. That fluid has to come from or go somewhere, which is the accumulator (reservoir).
The KDSS piston(s) won't heat-up like a traditional suspension shock. When the piston is 'locked', it won't move and won't generate heat. When the piston is 'free', it won't generate heat unless the piston velocities are extremely high such as creating cavitation due to pumping the fluid too fast. It's more likely that piston velocities may exceed allowable seal velocities and create leakage through friction/wear vs. heating. The piston is limited in velocity due to the valve being open or closed, and due to the shocks of the vehicle limiting suspension velocities. I'm guessing that Toyota thought about these things before putting them on, and the 4Runner is not the first Toyota vehicle with KDSS so it is 'tried and true' for Toyota.
Note that Toyota put the 2010 4Runner with KDSS through the paces. They ran parts of moab, rubicon, and the baja 1000 (where it rolled, breaking the ADD [automatic axle disconnect], running in 2WD for the remainder and still finishing). Here is the rolled vehicle with KDSS intact being driven two years after baja:
https://www.youtube.com/watch?v=fJwLeYHTwDw&feature=youtu.be
(skip to 1:08 to see the rear piston still connected)