Media safes are a very good idea. The differences compared to most commercial safes isn't just a mater of internal temperature. most commercially available safes use gypsum cement as insulation. This is the same stuff as the inside of drywall. It is a very good fire barrier. In part because gypsum contains, even when dry to the touch, a large quantity of water trapped in its crystal structure. For a fire to get through drywall it has to boil off all the water before the temperature can rise past 212F. Even after the water is gone the dehydrated gypsum is both non-flammable and a poor conductor.

While in most cases drywall releasing water vapor during a fire is not a problem in the case of a safe it depends on what is inside. Paper, and many other materials, can stand a considerable amount of vapor and steam. Computer media, particularly the older 4.25 and 7.5 (remember the old floppies? Way back when a fast CPU operated at 50Khz, memory was measured in KB and a large HD was 100MB. LOL) discs. CDs and DVDs can melt, warp, or corrode. The clear side isn't as sensitive as the thin layer of aluminum under the painted label. That delicate layer of aluminum can corrode. You can see it when it has happened. The disc turns grey and black.

Media safes are designed to keep the insides cooler and, because they don't use water containing gypsum as insulation, drier. So they don't warp or fuse and they don't corrode.

There are media rated safes out there. Be prepared to pay through the nose for a media safe. A cheaper alternative is a media rated box. This is essentially a smallish water-tight insulated box that is designed to go inside a fire safe and make up the difference between what a regular fire safe does and what the media needs. These are a lot more affordable than a complete safe designed around the media standard.

These are available at many office suppliers. If they don't have them on hand they have them in their catalog and can order them.