Maybe I misunderstood, as I have worked on cold, dry storage facilties before, to include mission critical and anticipated requirements for contingenercy emergency power.
While you may want to do hand calculations for envelope, amount of temperature rise will depend heavily upon ambient conditions and the storage contents and their temperature. I've seen this same question asked in customer meetings with the COE when they needed to have a contingency contract for an 18-wheeler to drive up within a specified time frame for emergency power and 4 days operating fuel. Perhaps picking out worst case, say July 19 at 1500, and only thing left in cold storage is mission critical only (such as as panedemic supplies included with MTOE deployables). This is not a routine or simple solution, at least if that is the case.
Most surprsing is that the cold, dry storage facilties would be suppled with only EEC power, not full back up.