"If you wanted to heat the house to 18C, instead of 20C, (raising by 21K instead of 23K) you would only need 13 x (21/23) kW = 11.87 kW. If you now wished to raise the temperature to 20C, do you have to supply another 13kW on top of the 11.87, i.e 24.87 kW?. No. you have to supply an extra 1.13 kW."
Reflect on this:
You range rate your boiler to 11.87kw and wind the room stat up to 30C, what happens?, the boiler will run continuously until the house temperature reaches 18C but because the house is loosing exactly the same, then the boiler will still run continuously to maintain this 18C but the temperature cannot rise any further.
You now want a house temperature of 20C so you wind up the boiler to 13kw, what happens?, the boiler now has another 1.13 kw to get the house temp to 20C, from 18C (which requires 11.87kw continuous) it can't rise the temperature any higher after reaching 20C but will continue to run continuously at 13kw as the house is loosing exactly the same.
Having the room stat set to 20C will result in a average house temperature of 19C with a resultant average boiler demand of 12.15kw but in cycling mode.