Does it have a limit-stop on the hot water? It could be that if you remove the cover there is a piece inside that determines how much of the hot water is allows through. If it is set at the minimum setting, it would cause the problem you describe. Each faucet brand has a slightly different system, but you can find out how to make adjustments on their websites.

Thanks for the suggestion--will check it out.

collage-
Turning up the water heater temperature does not make much of a difference in your bill if you are looking to obtain a particular hot water temperature. You are either using a certain volume of hot water at a lower temperature, or a lesser volume of hot water at a higher temperature. The only significant loss is if the tank is poorly insulated because it will be radiating a lot more heat to the surroundings while it is on standby than at a lower temperature. Overall, lower temperature is good because you will still have a little less in standby losses regardless of the level of tank insulation, and it does reduce the risk of scalding injuries. But your energy usage for the situation you describe is not going to change your energy bill very much at all.

"When set at an appropriate temp, the water in the shower closest to it doesn't get hot enough to comfortably shower. " = Does this mean the shower "faucet" is a thermostatic? A pressure-balance? Or two handles? What is the water turn on mechanism? What is the mixing mechanism? What kind of valve, system, method, mechanism?