What parameters are to be used to determine how the time interval is varied? I've never heard of variable intervals in control loops (and I do this for a living)..... but that doesn't mean they're not out there.
When tuning a loop, the time interval is usually the first thing to get set.... it stays constant and is linked to the system's hardware. As long as the system doesn't change dramatically (in this case: volume of water being heated, heater element wattage, etc), the time interval should stay constant.
The general rule of thumb we use is (initial) interval=(time from ambient to 80% of target)/10, which usually gets us in the ballpark.
Unless.... someone else has heard of this?