Why does the Hertzsprung–Russell diagram's x-axis go from large temperatures to lower?
Originally, what was plotted was luminosity against colour, and by colour I mean the wavelength of the peak intensity. Short wavelengths on the left, and long on the right, as you would expect. 



Now since stars emit (nearly) black body radiation, there is a close relationship between colour and temperature. I suspect that the reason that the x axis isn't inverted when temperature is used is just inertia:- We have always plotted out H-Z diagrams like this and we will keep doing so.