The boiler thermostat only controls the temperature of the water leaving the boiler. This water circulates around a coil inside the cylinder and heats up the water inside it. However, once the hot water cylinder is at the set temperature, the cylinder thermostat (usually in conjunction with a motorised valve) should shut down the heating process.
Even if the boiler thermostat were faulty and was actually boiling the water, once the cylinder reached the set temperature the supply of water to it from the boiler would be switched off, and so the cylinder wouldn't get any hotter than the temperature set on the cylinder thermostat; it would just get there more quickly.
However, heating hot water in a cylinder is not an exact science. There will be a big difference between the temperature at the top of the cylinder and the bottom. Situating the hot water cylinder thermostat about one third of the way up from the bottom is usually the best place to get an average reading. But expect it to fluctuate.
If you were to remove the cylinder thermostat, and touch the metal underneath you will probably find it's not actually all that warm and not 60 degrees. It will be much hotter at the outlet pipe at the top that supplies the taps, and the thermostat will have been calibrated to take that into account, but as cylinders vary in size and shape and the cold water inlet temperature coming in may vary, all of this will have an effect on the final hot water temperature.
If the water really is too hot try turning the cylinder thermostat down, if it's still overheating then, there is a problem somewhere, but it won't be the boiler thermostat.