This Fire Test doesn"t use particles, and the flames themselves are not textured.
Here is the trick : The flames are made of an animated mesh. It is a sort of crown animated by Displacement Modifiers using a cloud texture for the displacement, referenced to an Empty moving vertically.
The fire effect is given by a texture applied to a Lamp using the same Empty as coordinates reference.
The material of the flames is completely transparent and specular. The light texture is only visible in specular reflections, allowing much more random and avoiding to show the limits of the mesh shape.
A very simple compositing is done with only Vector blur and a bit of ordinary blur.