A few things have come to mind about Harry and his relative lack of modern amenities.
The first is that a number of the suggestions provided so far would either not work, or could potentially work but might cause other problems.
One of the suggestions was to utilized a gas-fired hot water heater. I forget which of the later books it was, but Harry quite specifically mentioned it being too risky for him to have a gas-fired hot water heater, because there was a risk of explosion. As has been observed repeatedly, Harry tends to hex things, and he's therefore rather hard on modern appliances. This includes hexing mechanical devices like automatic weapons. With the example of a gas-fired heater, there is the possibility that the pilot light could snuff out, and there would be a build of gas, or any of the other potentially very bad things which can happen with such a volatile fuel.
For the example of staying in residential hotel, the wizard is most likely still going to be in close proximity to the hot water tank, or the hotel might very well use a tankless system, with the heating elements relatively close to the individual showers and faucets which would draw hot water. This is the case (both in terms of hot water tanks and tankless systems) because there is a limit to how far hot water can be moved from the heating source to the end point of use, and have the water stay within an acceptable temperature range (~120 degrees F) Now the greater the distance, the more material the water would come into contact with to draw heat from the water. This could be gotten around but increasing the water temperature at the tank, but then those showers and faucets closer to the tank would get hot water which is too hot, potentially 160+ degrees F (the temperature of a hot cup of coffee)
Now for Harry's issue of taking cold showers, I suspect that is a bit self-inflicted. The ancient Greeks and Romans had showers, and for a long time, various types of baths were available for people to use which could be heated. Unfortunately for Harry, he lives in a basement apartment of an old Chicago rooming house, and he has neither the money nor the craftsmanship to buy, modify or build some of the systems which could allow him to regularly take hot showers.
Consider this, Harry has a fireplace which he uses to heat his apartment. If there were a series of circulation pipes running between a water tank and the back of his fireplace, Harry could both heat his apartment, and have a source of hot water. Taking things further, by having a large tank of heated water in his apartment, it would actually help regulate the temperature of his apartment, since water is slow to both heat and cool. In order for his to be able to actually use this though, there would need to be a certain amount of re-plumbing the pipes...
For those looking for other, non-magical and non-technical ideas, look at how current groups like the Amish manage to live with, or some of the ancient civilizations like the Greeks and Romans. Some of the earliest examples of indoor heating and plumbing can be from such societies.
-Cheers