Couple of thoughts. 1) you could have an element out in an electric tank. Typically, all of your water would only be lukewarm, but it's possible that the shower uses a larger pipe that's drawing down the hot water faster. Have you noticed a large increase in your power bill? 2) your pipes to the shower might not be sufficiently insulated, while the others are.
When you say it'll scald you, do you mean if you use them at the same time or that the water out of the other faucets is really hot while the shower is lukewarm?
1) I think the tank is gas...though honestly I have no idea. Last night Mr. Mellamur turned the temperature up but that didn't seem to do any good. Power bill, it's higher but not significantly so. Though we've only lived here since October so I could be wrong about what's significant.
2) Exactly - water in the kitchen sink is so hot I can't put my hand in it. Water in the shower (in the bathroom off the kitchen) is tepid.
I would think that even if they are not adequately insulated, after running full-hot for a while it would come out hot simply because it heated the pipes enough. Seems like it would have to have a VERY long run to lose that much heat. I wonder if it's a problem with the mixing valve, letting too much cold water in.
Where's the mixing valve? Is it somewhere in the pipes or part of the water heater?
Part of your shower fixture...also called a thermostatic valve. It's in the wall behind the handle you use to control the water flow. I'm no plumber or engineer, though...so it's only a guess.
If you have a single-valve shower, that's actually a pressure balance valve, not thermostatic, but could potentially be the problem. If you're not getting enough pressure from your hot line, the valve will make it up with cold water, so it will never warm past a certain point. If you do have a thermostatic shower, then you have one valve where you set the water's temperature, AND a second (usually smaller) handle that turns the water on and off. If you do have that, then the cartridge in your valve is bad and isn't calibrating the water temp correctly anymore.
Either way, you need a plumber to get in your valve--usually the cover plate screws onto the rough inside the wall, so it's not too complicated to do that. Depending on what the problem is though, you may be ordering a small replacement part, or an entirely new valve. Either way, it's going to help you to know who makes your shower valve & trim (this is assuming it's the shower valve and not the heater, and I'm not a plumber either. Just sold plumbing for many years).