Mixer taps are not simply mixing hot water at temperature H and cold water at temperature C. The temperature H which your hot water source is capable of reaching is highly variable and certainly not constant. Higher flow for example reduces temperature as more cold water cools the heater. Heaters also cut out and oscillate as they overload.
Throughout the year the C temperature may also fluctuate by several degrees in a way that can trigger non linear effects in the hot water generator. (This is all assuming you have a just-in-time hot water source of course — more common in Europe than, say, NYC apartment blocks.)
Study the whole system and be prepared for unexpected non linearity everywhere. Heat loss per foot of pipe is a real thing, as is thermal damping of uninsulated tubing, to give two more examples.
If you can model the system then next up, you might try your hand at predicting the weather.