I support innovation2's description.
The "design" MDMT is that specified by the vessel owner. The "rated" MDMT is that found from applying the rules of ASME Code. For example, VIII-1, Figure UCS-66.2 is the flowchart diagram showing the rules for determining the lowest (coldest) MDMT without requiring impact testing. The concept is analogous to pressure: there is a "design" pressure specified by the vessel owner, and there is the "rated" MAWP found by applying the rules of the Code to determine the maximum pressure that the component(s) can sustain. In both cases, pressure and MDMT, there will be a governing component...that with the lowest pressure rating for chamber MAWP and that with the highest (warmest) temperature rating for the chamber MDMT.