as pointed out by duncelot this will only work on fire based spells.
As for the healing III resemblence the focus effect to look for in that regard is Improved Damage IV.
If you have ID IV then HT will do extra damage. But not with this focus effect. ID IV is 20% damage increase though.
There is another focus effect that is 30% increase in damage and will work on harm touch its called "Fury of druzzil". Its magic only focus effect just like this being fire only.