A cross-over between the hot and cold supplies somewhere will dilute the hot water further down the line. Fluids are weird...like many things, they take the path of least resistance...if you have a defective valve somewhere that allows it to mix hot and cold, that warm water will then supply things along that path of least resistance. Essentially, to eliminate that, you need to try to isolate that cross-over point. To do that, if you can shut off either the hot or cold going to a valve, it can not cross-0ver. It wouldn't be in the tub/shower valve unless it is a thermostatically controlled valve, then the cartridge could be bad. If there is another shower in the home, it could be that one. With the shower running, if you feel the cold supply lines of the other fixtures (vanity, kitchen sink, etc.), if one is warm, that valve is probably leaking (crossing over) between the hot and cold.
One thing some people do is put a Y-connection at their washing machine to always get warm...this creates a cross-over.