Boilers can be set to heat water faster by turning up the thermostat that regulates the water's temperature while avoiding drawing more water than the recovery rate for the unit. The recovery rate is the amount of water that can be heated to 100 degrees Fahrenheit in an hour.
Raising the overall temperature of the water by raising the thermostat setting means that less hot water must be used in the system to achieve temperatures lower than the setting. This decreases the drain on the boiler, which leads to less cool water being needed to keep the boiler filled. With less cool water added, the temperature of the water inside the boiler remains hot, and the newly added water is heated to the overall set temperature at a faster rate.
Other factors affecting the speed of heating the water include the size of the water tank. The larger the tank, the more water that needs heating as the water level lowers, which means the heating process is extended. The higher the recovery rate, the faster the water is heated as well, though the recovery rate is set not by thermostat levels, but instead by the actual manufacturer of the boiler. Units with higher recovery rates are more expensive to run, as more energy must be applied to heat the water faster.