“Ah, no. And for a fusion plasma, the actual amount of heated material is far, far less.”
True for magnetic confinement but not for inertial confinement.
For inertial confinement, the amount of material being compressed is measured in milligrams at most. If you figure an energy density scale up of a factor of a million for fusion over chemical reactions, the amount of energy generated per shot is on the order of a few kilograms of gasoline. Like as much as is released in a typical Hollywood car-explodes-on-impact stunt.
In the NIF (National Ignition Facility) the target chamber is a sphere ten meters in diameter, made of four-inch-thick aluminum. It is evacuated to a high vacuum before each shot. Its total volume is about 15000 cubic feet. I'm guessing it can handle the power output of a shot.