The problem is that the fire deity thing depends on which source you read. Some equate him with Loge/Logi, other's consider him a different deity. (Also, if Loki=Loge, then the whole Utgårdaloke eating challenge becomes very weird.)

And then there's the whole issue of whether or not you can lump all Jötnar in with the hrimtursar/Frost Giants, since there are eldjötnar/fire Jötnar as well...