We just got a new water heater installed in the basement, and the temperature in the 3rd FL shower is not hot enough for us. However, the temperature in the sink faucet on the 1st FL is fine and gets very hot, so that makes me think that perhaps the water heater temperature is fine. Would you suggest taking apart the shower handle, or would your first guess be something else? Shower handle is single Kohler shower handle.
Single handle shower valves normally have some way of adjusting the "all the way hot" stop of the handle. In many cases it's just a toothed plastic ring under the handle that can be moved to the next tooth or two to make the water hotter. This is meant to be a safety feature so even if the handle is cranked all the way on you don't get scalding hot water.
Your new water heater might not be set for quite as high of a temperature as the old one, so you're two choices are to adjust the shower or adjust the water heater. Note that adjusting the heater temp might make all the two-handler faucets hotter, so consider that.
It's possible the installer set the temperature low because they are worried about scalding, i.e. They don't want to be liable if you get scalded.
If you have all joystick 1-handle valves, those are thermostatic and will protect you.
Meanwhile, this installer may not know about legionella. The trouble in Flint surfaced a problem that was little known up to now: water heaters are breeding grounds for bacteria, particularly legionalla. You should crank the temp to 140 F for that reason alone, as that kills it.