I would prefer a proportional control where the speed of the fan is proportional to the temperature deviation. This allows the fan to run continuously and more slowly and quieter rather than stop and then blast.
Yes, that's a good idea, but it will no longer be a beginner project. Proportional control of fans will save power, but for something small, it might not be worth the extra complexity.
My concern is noise, not power consumption.
Copying a proven design should not be complicated at all.
Even a simple design should not be complicated.
Really simple is to have two or three steps. Take a 12 V fan and run it at 0 V, 6V, 12 V depending on temperature.
But with an Op amp it should be very easy to design a true proportional control.