I was under the impression that dividing the wattage across a parallel branch would spread out the heat evenly. I'll hook it up tomorrow and go from there.
The tricky part here is that wattage is a product of Voltage and Current.
So... you have a 12V source, and an LM7805 regulator.
The regulator will be dropping 7V across is, and will have 500mA (made this number up for this example) passing through it.
This means that the regulator will be dissipating 7V x 0.5A = 3.5Watts.
Now, if you put the resistor in Parallel, it will have 12V dropping across it, and will allow an undisclosed amount of current through depending on it's value. This will dissipate additional heat, on TOP of the 3.5 Watts that the LM7805 is already putting out.
If you put the resistor in 'series' then the voltage drop across the LM7805 will be reduced by whatever the voltage drop across the resistor is.
In 'total' both will dissipate 3.5 Watts. This is the desired effect.
The only case that a parallel circuit would share the heat dissipation is in a constant current circuit... This would mean that 500mA would go in, and branch across any parallel branch. Your circuit, and vehicle however, is a constant voltage circuit. So Parallel circuits will always mean more current and more power dissipated.