Annie E rework [Concept]

Many people (myself included) have looked at 's E and felt like the spell was odd on a burst mage like her, a defence spell on someone who is typically really squishy is kind of strange. At the same time, Her Q, W, and R all are plenty for her kit, yet her E seems like a throw-away spell. More burst would definitely not be the solution, so a defence spell seems like a good choice, yet the current spell is just kind of bland and boring. A t most, someone takes a hundred damagee from her E in return for Annie's death. Mobility would also be a bad thing to put on Annie's E seeing as that would break her for the most part, and more CC in any form would be absurd, so here is my idea.

E: Burning Aura. For the next 2/2.5/3/3.5/4 seconds, Annie increases the temperature of the air directly around her (radius of 150 units) burning anyone nearby for 5/10/15/20/25 (+.15 ap) damage per second. This spell is also casted on tibbers if he is sumoned dealing 25% less damage, but with a radius of 250 units instead. Mana: 40/45/50/55/60 Cooldown: 13/12/11/10/9 seconds

The idea behind this is she no longer takes reduced damage, but the spell is pretty similar to the old making it easy to adapt to. The spell also can be used in a similar way to the old one to stack up her passive without enemies nearby, but not be a huge waste. (Plus you wouldn't have to change the particles much at all! Maybe a faint line as an indicator, but idk) I just felt like this spell could be a but more fitting for annie without changing her kit drastically and also feeling a bit more a fire mage might. (Because really, by would ashe sending an arrow hundreds of units away allow for annie's shield to burn her?)

I understand this probably won't happen, and if it were some damage number would have to be tweaked on her other spells, but it was an idea I had. what do you think? Too strong, too weak, or do you prefer her current E and why?