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Except that you're right that watt is a unit of power you've got it mixed up. Watt is joule per second, and joule is the SI unit of energy. So it's a watt times second which is a unit of energy, not a watt per second.a watt is a unit of power, not energy. A watt per second is a unit of energy
So watt per second is the unit for rate of power increase, not for energy.
Perhaps in your part of the world. Most of the rest of the world is metric, and there the common unit for heat is J (joule). Or kJ, MJ, GJ etc. One BTU is rather close to one kJ (1.055 kJ, to be more precise).BTUs (British thermal units) are more commonly used to quantify heat.
EDIT: Dang, this thread is moving fast. Two other answers just during the time I used to type mine on the phone