Caster Level?
Cast Level?
Character Level?
The main use for this I could think of is to heighten spells - which means it would be Cast Level. But when apply BurnIt extra fire damage it was clearly functioning as Character Level (workaround is to use half odd CL - but that does not work if you are using it at a lower cast level)
Normally Cast Level heightens both die and constant damage, but seems not available to multiply die?