I was questioning Muggles assertion that heating up a house slowly (to reach a set temperature) is more gas efficient and comparing it to accelerating a car slowly or quickly to achieve a set speed. It was only the comparison why I found flawed.Well actually, I think you should.
You're the one that said Muggles was wrong. Perhaps you should explain more fully why.
I agree that running a boiler at lower temperatures will improve its efficiency due to increased condensation. But it will still need to provide the same amount of heat whether the house is heated in 30 minutes or 3 hours. Whichever method is used, the heat input has to be greater than the heat loss or the temperature will not rise. There is, of course, a limit as to how slowly you heat a house.
If what Muggles (and, presumably, you) say is true, Honeywell etc should be designing their controllers so they heat the house up slowly; but they don't. They engineer them so max output is provided initially and the boiler is only backed off when the house is within a degree or so of the required temperature. I'm not sure what happens when weather comp and Opentherm controllers are used.