Custom made PID for coffee machine

Hi All,
What I would like to achieve is regulating the temperature of the water inside an espresso machine's boiler in order to achieve stable brew temperature.
The way the boiler is build is a cast aluminium bloc with a built-in heating element, and a temperature probe on the bottom of the boiler on the outside (no contact with the water inside the boiler).
I came to the conclusion that I probably need 2 sets of PID values, for the following 2 scenarios :
- The machine is making coffee, meaning that hot water is pumped out of the boiler and fresh cold water is entering the boiler
- The machine is not making coffee

Now, I can probably come-up with the right PID values after some experimentation, but all this is going to ensure me is that the walls of the boiler are at the set temperature.
My question is, how can I design a system that will take into account the way the boiler temperature rises or drops in order to come-up with an indication that the water inside the boiler has reached a stable temperature ?