The problem with espresso machine startup is that there is 1.5kg piece of metal (grouphead) through which flows around 60ml of water from the boiler. What do y

The problem with espresso machine startup is that there is 1.5kg piece of metal (grouphead) through which flows around 60ml of water from the boiler. What do you think is the relation between boiler water temperature and the water that actually reaches coffee? When the machine starts, the grouphead is cold. If you want to get good brewing temperature you need to, either a) Wait for 40 minutes until grouphead heats up slowly and everything stabilizes b) Heat up water for 10 minutes and then pump a lot of water through the grouphead to get it hot from the water and pray everything works well c) Build a model that will predict correct setting of water in the boiler given predicted temperature of the grouphead so that when you push water through the grouphead it cools just the right amount. Unfortunately, the correct brew temperature is 92C so you only have couple of degrees to work with. But, still, heating the water to higher temperature causes grouphead to heat up faster and you don't need to heat it as much because it will receive hotter water. Commercial machines do not have this problem because they are started in the morning and only turned off for the night and they have huge tanks of brewing water in them so inflowing water does not affect the temperature so much.