The controller of a water heater usually has a high hysteresis, keeping the temperature within the range of a few °C.
If you need more precision, you can build something on your own. It is simple to switch the power of your heater on or off. Maybe, you have a look at this application note about zero crossing switches. These devices contain an opto-coupler to insulate your circuit from the mains and a control unit which switches the AC mains during its next zero crossing. The benefits are less EMI and less power dissipation, and of course you do not have to do much on the mains side. On the other side, this devices switches the current for entire half-waves only, so if you want a "duty-cycle" of 1%, you need to switch one half-wave of 100, which results in a period of 1 second (for 50Hz mains). But this is not such a problem in your case.
The document also contains an example circuit for temperature control, which is a good starting point
BUT a water heater contains some volume of water, and it takes some time until the heat from the heater spreads into the volume. This can lead to heavy oscillations of your temperature. The built-in thermostat is so slow that this does not happen.
For a well-regulated temperature you will need some kind of PID-controller which controls the heater based on current and previous temperature measurements. While a PID can be designed in analog electronics, a microcontroller can be used as well, and it may be preferred by you, as you have a high reputation at stackoverflow...
Implementing a PID in software is easy, the hard part is finding parameters for which it regulates your temperature as fast and precise as possible, without overshooting / oscillations.
Another point: Depending on the size of your water reservoir, the water may form levels of different temperature. Maybe, you think about a way to circulate the water inside the reservoir for a more homogenous / faster temperature distribution.
By the way: You say 5-10KW, which is quite much and usually not taken from a single phase, but from a three-phase system, and you need to switch the three phases.