Will weather compensation reduce my energy consumption?

Weather compensation systems aim to keep the occupied space at a constant temperature, for example 20 degrees, they do this by matching the heating output to the losses of the room/space at a given outside temperature. Traditional central heating controls tend to over and under shoot the set point leading to larger variations in room temperature. If you plotted it as a graph it is the areas under the peaks and troughs above and below the set point that energy savings through weather compensation can be made.