3ohm coil of .28 Kanthal being pushed at a higher voltage to heat as fast a 3ohm coil of .20 Kanthal won't result in the same watt output and could burn the juice. Watts law is a theory base on perfect conditions and we're applying it to a world with imperfect circumstances (thicker wire takes longer to heat up).
If a vaper is calculating the amount of watts they want the coil to output, applying a higher voltage to heat a stupidly long and thick coil up faster but ending with incorrect (approximate) wattage and burnt juice makes no sense unless you've got a Janty Mid-style system that blasts a coil with 8.4v then jumps down to 4/5/whatever volts.
I get where you're trying to go with this, but I think it came out all wrong.
Watt's Law is not a theory...that's why it's a law.
1 watt is always going to be 1 amp at 1 volt, no matter if you are trying to heat 1 ounce or 1 pound.
What you are talking about is thermal inertia; the amount of energy that is needed to get from A to B (in this case A & B are temperatures) in a certain amount of time. More mass (thicker or longer wire) will require more energy than less mass to achieve identical acceleration, just as it would take more energy to throw a bowling ball at the same speed as a baseball. The problem is what happens when you reach the desired wire temperature. Other than the Janty-Mid, no other APV's can throttle back the power, so you would usually overheat the coil and burn the juice. The only solutions are either a really good juice supply (how else would 20+ watts on an RBA/RDA taste as good as it does) or you deal with the lag time of a slow heating coil.
