This will requires a few different smoke simulations with Force Field effects. Probably would have to composite them together at the end for best results. See video example:
So, here are two renders with different intensities on the material. Trying to get the gradiant from white to yellow to orange to brown as the photo above does.
One thing I like to do with “fire and smoke” is to render several different versions, then composite them together in a fairly-random fashion. Alter the speed of some of the strips. Start and re-start them at different points in their timeline. Freely play with opacity. Tint one. The sky’s the limit. You get a very chaotic effect that is very easy to control and cheap, since once each piece has been rendered (to a MultiLayer OpenEXR file), it’s just 2D post-processing from that point on.