Here is what I was thinking:
Instead of using crystalized heat to level items, we could instead use it for UV's. When an item is ready to be upgraded instead of just using the alchemy machine, knights can go to the anvil near the barracks and use crystal heat on an item there. Crystalized heat will not guarantee a UV but will increase the chance to receive one (max chance 60% or 65%). Keep in mind this only works for ONE unique variant.