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The boiler will not need to run at 13kW once the house is up to temperature.From my (limited) understanding, my property's heat loss, is calculated at an external temp of -3C and in internal temp of 20C. Let's say for example the total is 13kW. My boiler will need to run, on average, at 13kW to maintain this constant internal temp of 20C, assuming all other factors, including the external temp of -3C remain constant.
Let's say the house has got up to temperature so the room stat has turned the boiler off. The room temperature starts dropping and when the temperature has dropped, say 2C, the room stat turns the boiler on. The boiler now needs to raise the temperature by 2C, not by 23C (from -3 to 20), so only 1.13kW is required (2/23 x 13). Unfortunately most boilers only modulate down to about 5KW.