Ken what a watt is can be a bit confusing I admit. But apart from the mathematical relationship Monte (I think) gave you, Here is a practical (I hope) explanation.
The Watt is a measure of power. It is the Watt what does all the work.
The Ampere, the Volt of the Ohmic resistance do nothing on their own.
If a certain wattage is needed to do a thing, then that is what must be provided. Within reasonable limits it doesn't matter what the voltage is, it doesn't matter what the current is, it doesn't matter what the Ohmic resistance is.
Those reasonable limits would mean that a very High voltage is not desirable because of safety, insulation/ arc over problems.
In the same way, very High currents are to be avoided because of the risk of overheating the wires used to carry the stuff, and the need for larger cross sectioned conductors of higher conductivity.
Have you heard of 66KV +++ transmission lines? Those Extra High Voltage Transmission lines are feeding a City, even a State. Imagine the power that these lines are called upon to carry.
If that power were to be supplied using 240V, refer to Monte's formulas,,,Current = Power/Voltage, then to supply the megawatts needed by a city, the current is going to be very high and the cross sectional area of the conductors will need to be impracticably large to avoid severe losses. However at 66KV and higher, the same power can be delivered at considerably less current, hence smaller /lighter cables.
Ken if you are interested, you might like to look at this link:
http://www.powercor.com.au/docs/education/sheet_f.pdf
So to come back to the point, power (Watts) is what is going to move your objective temperature from ambient temperature to some value above ambient.
12v at 1 amp and 12 ohms will give 12watts. 240V at 0.05 Amp and 4.8K ohm will also give you 12Watts. 1volt at 12 Amps and 0.083 ohms will give you 12 Watts. So theoretically the same power can be delivered by various combinations of voltage and current, but in practical terms we must choose wisely what we will use. Anyways I've probably prattled on needlessly, it is a big subject to tuck under your belt overnight, however you might gain much understanding by studying the material at the link I provided.
cheers,
Doug