From what I've read, ammunition which is not contained in a firearm barrel isn't much of a threat. As soon as the powder starts to burn, the seal between the casing and the bullet will be opened, allowing most of the gas to escape harmlessly. In an experiment where rounds were placed on a metal table which was heated until they cooked off, casings usually travelled less than a foot. In some cases, the bullet stayed attached to the casing and the primer went flying (after which all other gasses vented out the primer hole). The primer could fly some distance, but because of its light weight wouldn't pose much of a threat.
Thanks SC. Sounds like this is what might have happened. I heard there were a couple of loud 'bangs' and hot ash went through the chain-link screen in front of the fireplace, landing on my little sister.