Step 1: Leaps and Screams
No. The water remains as cold as a cod fart. Since you're child of your time, you guess that the machine on the wall must be programmed in some way. Before you reach it, you have time to get worried about your smartphone: Was it quad-band or only tri-band? Will it be able to interact with the heater?
Wrong. As you can see in the picture above, there is ample reason to despair. The dumb thing does not even have a power on button. (No, not even on the sides that are facing away from the camera.) Well, "one dot" and "two dots" are at least labels that are gender neutral and perfectly incomprehensible regardless of cultural background.
You give up and call one of the natives. After some battle tank gearbox noises in your ear, you have learned that the thing is fully automatic. You just have to open the tap some more, then the heater is turned on. The native explains that a "Durchlauferhitzer" heats the water on the fly (swim?), as it passes through the thing. There is no reservoir with hot water.
With new hope you step into the shower and open the tap, some more, then some. When the flow rate rivals that of the river Rhine, the box on the wall finally goes "clack". Within seconds, the water goes from "cardiac arrest" to "cerebral haemorrhage", and you slam the tap shut in self defence.
After experimenting for twenty minutes, your performance remains erratic. The machine goes "clack" or "thunk", that is, turns the heat on and off, respectively, virtually at random. Most of the time, the water actually gets colder as you open the hot water tap more, but sometimes it can suddenly become much, much hotter. What's the deal? Who invented this piece of <censored by the instructable team>? Is he still alive? If yes, where does he live?
Stay cool. I'll explain everything in the following steps. Above all, don't scream and throw the thing out the window, your neighbours will call the police. (...not because you vandalised the bathroom of your flat, or because you threw the "Durchlauferhitzer" on the street, the Germans do that all the time. No, they'd call the police because you screamed.)
Step 2: One Dot Theory (and Practise)
In the heater, the water flows through a flow rate relay. It consists of a constriction combined with a differential pressure switch bridging it. When the flow through the constriction is large enough, the pressure drop over it will be sufficient for the switch to close. The relay is, you guessed it, connected to the heater.
The heater is a simple resistive electrical heater, with constant power, typically a handful of kilowatts. Now, since the power is constant, but the flow through the heater varies, the resulting temperature depends on the flow rate. To be precise, the temperature will be inversely proportional to the flow rate, once the relay has activated the heating element (see diagram above).
This explains some of the frustration in the shower. As you turn the hot-water on, first nothing happens. Then, "clack", suddenly it's too damn hot. Well, judging from the diagram, the solution is to open the hot water tap some more. Counterintuitive, sure, but that is how it works in reality too.
One interesting consequence is that as long as the flow rate through the hot water pipe is large enough to keep the heater on, it does not matter if the water at the shower head is a mixture of a small amount of water that came through the "Durchlauferhitzer" and a small amount of cold water, or a larger amount of water that was heated, as long as the total flow rate at the shower head is the same. That is, the cold water tap and the hot water tap has the same influence on the temperature!
So, a good strategy is to open the hot water tap generously straight away in order get past the peak quickly. The diagram really shows the situation at steady state. The peak will not be as hot if you rush past it.
Step 3: Two Dot Theory
The second heater is activated at a higher flow rate than the first. The resulting characteristic is shown in the diagram above. If you are an shower greenhord, and are unfortunate to step into a shower cabin powered by a "Durchlauferhitzer" that is in its two dot mode, you will have some serious fun. Not only is the flow rate - temperature characteristic discontinuous, and the slope mostly negative, you will be thrown off by the time lag between your commands and the temperature change at the shower handle.
If you are lucky, you can hear the "clacks" and "thunks" of the heater. The worst case is when the heater is in another room. You cannot hear a thing and will have to learn to shower like Yoda.
The bottom line is, if you can get enough hot water in the one dot mode, forget about the two dot mode.
Step 4: Extra Credit
Thermal Mass 1
In Germany, pipes and cables are often buried in the plaster of the wall, with no isolation around them. This gives the pipes a substantial thermal mass. If you start your shower by making your hair wet, followed by a short pause where you shampoo your hair, you are in for a big surprise. Even if you had the water turned off for only a few seconds, the first spurt of water you get after the pause will be as cold as the wall in which the pipe is laid. A considerable amount of water must flow through the pipe, and the wall, before this effect fades.
Thermal Mass 2
In the heater, where the water is heated, the water flows through a curvy channel of copper. The thermal mass of this part of the heater can manifest itself through a painful surprise. The heater coil side of the copper channel is quite a bit hotter than the water side at steady state usage. If you start out at a flow rate close to the "thunk" threshold, where the water is at its hottest, and then abruptly shut the water off, additional heat will flow from the electrical heater coils to the water in the copper channel. If you turn the water on again within the next few seconds, you will be awarded with a spurt of increadibly hot water. To be perfectly honest, it is not water anymore. The substance which is produced in this way, is more adequately described as plasma. After you are done with your shower, you can toast bread on your naked skin.
The More the Merrier
This is a no-brainer. If the "Durchlauferhitzer" is connected to more taps than those of the shower, you are in for some serious fun. Your efforts to outsmart the heater will be utterly futile, as soon as a second person becomes part of the equation. He/She can increase the flow through the heater above the second threshold, or, just as bad, steal some of the hot water. Consumtion of cold water can also upset the carefully adjusted equilibrium of your shower. A liberate consumtion of cold water can lower the pressure available to your heater. Unless you adjust the taps, the flow rate may drop below the threshold. The header goes "thunk" and you will scream and jump anew.
If the hot water and cold water are lead through a common exit, you can turn off the heater by increasing the cold water flow. The reason is that the outflow is becoming blocked by the cold water flow, thereby reducing the hot water flow. If it was close to the threshold, the heater may shut down.
The most interesting nonlinear effect I have ever noticed, is one that was caused by the thermal expansion of the tap. When heated, the spindle in the tap expanded and restricted the hot water flow. If carefully adjusted, this change was enough to turn the heater off. The water cools and the tap spindle too. The flow increases and the heater is turned on. We are back were we started.
Step 5: The Future of the "Durchlauferhitzer"
The modern day heater has several buttons, an LCD display, and the user can select one of several operational modi. The top models even have a wellness mode. In this mode, the temperature changes periodically between too hot and too cold. Yep. Here in Germany, people think this will improve their immune system.
Health through pain. A popular concept that refuses to die.