Casks shield materials and passively remove heat via heat transport paths from deep inside to outside the cask. The transport path may be heat pipes and conductive rods that are non-linear so that radiation is always shielded by the cask. A damper may surround an end of the heat transport path to control heat loss from the cask. A jacket of fluid or meltable material that conducts heat by convection may surround stored materials ensure an even temperature within the cask, and the heat transport path may absorb heat from the jacket. Casks are useable to safely store, transport, and dispose of any sensitive or heat-generating material. Casks may be opened or closed to simultaneously load and offload materials at a consistent operating temperature provided by heaters in the cask.