A good plumber could probably give you an answer in 15 minutes. It would be tempting to immediately blame the shower itself as it's the most logical explanation.
Personally I'd turn water off (assuming combi boiler this is enough, otherwise more care needed), open downstairs and upstairs taps to drain down (and allow air in to avoid a vacuum) and remove shower unit.
Then fit a 1/2 inch BSP to 15mm flexible hose to each side, and put a normal isolator on the 15mm end.
Then turn water on again, and try the hot side as a simple tap.
If it gets as hot as the other taps, it's the shower. If it doesn't there's a curious problem that needs further investigation.