Hi John,
Very interesting as you bring up a good point that brings one aspect of this question to light that i hadnt thought about yet, and that is temperature, especially that of the heat source.
The simplified electrical equivalent of a heat source and sink could be a voltage source and resistor and capacitor in series. Of course the total resistance and capacitance would be distributed along the spacial dimension say 'x', so it would be similar to a transmission line, but we can still look at it as a more simple circuit of just the voltage source, two resistors, and two capacitors (forming a low pass circuit) and with one more load resistor at the output. The joint we want to heat is the node of the first cap, and the node of the second cap is a unwanted sink we are stuck with because of the physical structure.
In the case of the small wires, we have a heat source and a certain thermal resistance and heat capacity, and the small wires conduct little and the total heat capacity is relatively small, so even a lowish temperature could raise the joint to the temperature required to melt solder.
But with larger wires if we increase the total power but done increase the temperature, by the time the conduction takes place to where we need it to be the temperature might be too low to melt solder.
In your example we have a large copper structure and we apply heat. If we have 100 watts of heat at a lower temperature it may never heat the joint enough because the conduction rate is too fast. If we increase the temperature and keep the wattage the same, we may actually get enough heat to the joint, because the transfer of heat is also dependent on time.
With a torch we have a very high temperature to work with and that creates mildly hot localized temperature rise. With the same power but lower temperature the material may conduct away too much heat before the joint gets to heat up enough.
In the electrical circuit, it would look like (say) a 100v source and (say) two 100 ohm resistors and (say) two 10000uf caps. We have a 100 watts, but it's going to take time to raise the voltage at the first node due to the 100v source. If we increase the source to 200v we can get the node to change faster <rough analogy>.
So what this means is that i also have to consider the temperature of the source as well as the total power the source can deliver. If the solder gun gets up to 600 degrees C then the hot air itself must reach 600 degrees otherwise they are not equivalent. So now the question is just how hot do the hot air soldering tools air get:?
I'll search around a little and see what i can find out, but if anyone has any more info that would be nice too.