The first thing I noticed is that the renders look very obviously pasted. You can try blending them with the fiery background. I'm not sure if this will work, by try this:
1. Select the render
2. Go to Selection -> Modify -> Feather
3. Set to around 15 px
4. Go to Selection -> Select Inverse
5. Press delete
What this does is remove a bit of the border of the render, giving the effect that the flames are engulfing it instead of just serving as a backdrop. There may be other, better ways to do this, but I don't know any at the moment.