Does burn damage do double to ice enemies?

I just picked up Immolate, and I was wondering if the burn dmg would be double for enemies that have a fire weakness. For example, the way that flare or firestorm will hit for double damage against ice elementals or Oakhearts. I know Immolate's strike dmg will be doubled, but what about the burns?

I do believe that the degen will NOT be affected in any way. I would think 14 degen is a little extreme, and could not possibly be allowed by the game. Weaknesses affect the actual strike damage only, not DOTs.(actually burning is a condition)