Its not limescale like we get here in the south east which I'm talking about. Its scale on the primary side of the plate heat exchanger which could be the problem.
Over the years which a heating system is in operation, if the system was not cleaned initially, or not maintained to remain clean, metal oxides and flux residues can collect inside radiators and on the inside of the heat exchanger (not the side that the mains water goes through). These collect around the heat exchanger as the concentration of heat there, coupled with the very small waterways makes it an ideal place for blockages to occur. I'm not that great at describing the science behind the formation of scale in heating systems so excuse the basic explanation. Agile or someone can do this better than I.
When the plate heat exchanger is blocked, the 'scale' which I refered to earlier can trap latent heat, and act as an insulator. This causes both the mains water not to be heated right (as heat can't transfer through the insulating scale), and also cause the boiler to overheat (as heat can't escape anywhere, i.e to mains water like it should).
I doubt that its the diverter as normally when its to blame you have a situation where the radiators heat up on DHW call, or where the hot water doesn't heat up at all.