Basically I was using the forge to level up my sword when I noticed I could upgrade my Sentenza as well. However, my Sentenza wasn't fully heated, so I have no idea why I could level it up.
https://lh6.googleusercontent.com/-3IkyrgK2HGU/Uf32fBKvX9I/AAAAAAAAABw/i...
I've got another thing along the same line. If you've actually completed the level on an item, but haven't yet leveled it with fire crystals, it will still absorb heat. This results in my items that do need heat getting very little.