Now that we have all the pieces, we can put them together.
Assign a dielectric shader as shader node MR material. Assign a dielectric photonic shader as MR photon shader. Leave all dielectric values to default. The refraction is going to be distracting, so for now we turn the index to 0.
Assign a Parti Volume as MR volume shader and a Parti Volume Photon as MR photon volume shader. Since the ball is only partially filled with fire, set Mode = 1. Set the Scatter to a bright orange. To better see the medium, give it maximum Extinction = 1. For now, assign a fixed number to the height, which is relative to the sphere coordinates. My sphere is centered at 0,0,0 and has a radius of 5 so I can set any height between -5 and 5. I set it to 2.
We want a random height between -5 and 5 . The Solid Fractal is the random number generator with the most detail so that's what we'll use. But since it produces only numbers between 0 and 1, create a Set Range node, and set the Fractal's outAlpha as its value, 0 as old min, 1 as old max, -5 as new min and 5 as new max. Connect the output of the Set Range to the Parti Volume height. In the Fractal's placement node click Fit To Group.
We want a greater variation in height, so increase Ratio to 1. We also want less detail, which is determined by Frequency, so decrease it to 1.3.
The fire looks too uniform. We want a smooth blotchiness. Perlin noise generates random numbers with a smooth transition between values, so that is what we use.
The blotchines is too pronounced. Bring down the threshold to 0.28 to smooth it out more.
It makes sense to tie the color to the fire density. The less dense the fire, the darker and redder it will be; the more dense the fire, the more yellow and bright. The problem is that the noise that controls the density doesn't output color. Here is where the remap node comes into play. Connect the outAlpha of the noise to the value of the remap node. In the color section of the remap node, create a ramp with colors going from black to red-orange to yellow to almost white. The output value of the noise is the index to the ramp, so a low density value will correspond to the darker and redder values of the ramp, while higher density values will correspond to the lighter values of the ramp. Connect the outColor of the remap node to the scatter of the volume. The effect is subtle, but comes in very handy if we decide to animate the noise, to make the color follow it.
Finally, bring the dielectric index of refraction back to 1.3.