A good plumber might have an even better idea, but from a logical stance checking the hot feed to the shower is the aim and that's one way it occurred to me to do it. Depending on the details of the plumbing and the presence of compression fittings or john guest push-fit fittings there may be even easier ways.I just tried to take this in. Now I know nothing about plumbing but I assume a good plumber could do this in half an hour and rule out the shower? I could also check the pressure doing this?
I'd go on your local Facebook free/swap group and ask for a recommendation of a good local plumber who can help diagnose a problem with a mixer shower.