Shower temperature changes, but is the heater the cause?

What observations help narrow down temperature swings during a shower? Does it matter whether the change comes on gradually or suddenly, and whether it happens at just one fixture or at more than one?

I’m also curious whether the timing points anywhere useful: for example, does the temperature shift when another hot-water fixture is used, or when the heater’s burner is operating? What would make this worth stopping use of the heater and calling for service, rather than looking for a change in flow or demand elsewhere in the plumbing?