I'm having a little trouble following this thread, but I think the main problem here is that most of you are using the same unit both when talking about power, and when talking about energy. Power is measured in watts (W) or kilowatts (kW) and is a measure of 'the speed at which work is being done precisely at this moment'. Energy is measured in wattseconds (Ws), watthours (Wh), kilowatthours (kWh) and is a measure of total work is done over some time period, power * time = energy, 1kW * 1h = 1kWh
Mixing power (kW) and energy (kWh) is very common and many argue that is makes no difference as long as it's clear anyway what is talked about, but I think this thread is a good example of 'not clear at all what is talked about'.
'kW/h' mostly makes no sense, that would be a measure of "power acceleration", for instance how fast is the burner power increasing/decreasing.
I apologize if I misunderstood what this was all about...