I originally thought that you could not safely store CDs and DVDs in a fire safe. I was wrong!
I have learned that Sentry Safe in fact makes fire safes that are suitable for protecting CDs and DVDs from fire.
Be sure that the fire safe you select is in fact suitable for your intended contents. Not all fire safes are equal!
Their web site has a nifty search feature that allow you to pick the size of safe (chest, file box, wall safe, etc.), the items to be protected (documents, DVDs, guns, USB flash drives, etc.), and the threat (fire, flood, theft, etc.). For instance, here are the results for a search for file box safes suitable for protecting CDs, DVDs, and USB flash drives from fire.
I personally own a Sentry Safe similar to this one that I purchased from Walmart a few years ago for about $50 USD. This safe is suitable for storing CDs, DVDs, and USB flash drives. This safe even comes with a CD/DVD holder built into the lid (which mine did not). This safe is also waterproof. This provides me peace-of-mind, for if in the event of a fire limited to another part of the house, the safe were to get wet.