Based on my analysis the published image is too processed to be able to invert the colormap to get to the brightness temperature data. I had better luck with Paper IV Fig. 15. See: https://physics.stackexchange.com/questions/472641/what-woul...

Technically yes -- colormaps are 1-dimensional non-self intersecting curves in RGBA space. You just grab them by the... I mean just straighten them.

I don't know if an explicit formula for the colormap is given, but you can always do "xs = np.linspace(0,1,100); ys = { cm.hot(x):x for x in xs}" and recover an approximate inverse. Then apply this function to each pixel of the image.