Using Cold to Fire, does damage benefit from both fire and cold nodes?

Title says it: Say you use Freezing Pulse with Cold to Fire, does the converted damage benefit only from fire, or also from Cold?

EDIT: Also, I assume the Cold to Fire would stack with Avatar of Fire for a full conversion to Fire damage?

Yes, you can boost the converted part with either damage bonus, it's dealt as fire but is considered both damage types when calculating your damage output.

And it stacks with avatar for full conversion, yes.

Mind though that a node that'd increase Elemental damage would affect both fire and cold damage but not before the conversion.

So 100 cold dmg 50% converted with +10% elemental would be 55 cold and 55 fire.

Alright, thank you both very much. :)