First, you might use less power in the time you are heating the warmer water, but the sum of power and time will end up just the same as if you blasted away with all the watts you have. There is no efficiency advantage to heating water gently.
When you add the price of designing and building a proportional mode controller and subtract the nothing that you gain, there is no profit in doing this...not monetary profit, not ecological profit. Does that clear things up?
If you are just studying controllers, put up a question in "chat".
If you are going to build this anyway, someone smarter than I am will be along to help you shortly.