I think you are oversimplifying a bit. Perhaps read that Klippel paper I suggested. The heat is dissipated from the Voice Coil through convection and conduction through the leads, and to the pole-peice and magnet. This is spelled out explicitly in the Klippel paper. But, most models assume the time constant for the voice coil is much shorter than the pole-piece or magnet, i.e. they are totally not the reason the VC don't instantly burn up...
I'll leave the rest alone.
Hold on... I got thinking some more about this:
If it was so hard for a driver's voice coil, say a tweeter, to dissipate heat, it wouldn't take long at all to reach thousands of degrees with just a watt or two. If literally all of it wasn't transferred and radiated away rather quickly, tweeters (and speakers of all types) just wouldn't survive. There isn't a lot of movement in a tweeter, and very often the design behind the dome is entirely sealed. This means that, other than through the dome, nearly all of the heat (so nearly all of the power, as at 90dB/W, most power applied isn't converted to movement, but heat) is being conducted to the magnet assembly and then radiated to the environment. Since I've pointed my IR thermometer at many a dome's dome, I can say that their temperature is maybe 1 deg C above ambient at quieter listening. Domes in medium sized rooms never seem to rise to more than 10 deg C over ambient at comfortable listening levels (not quiet, just not painful).
Considering the above, most conduction
has to be to the magnet assembly, and most of it has to be pretty quick, because also, considering the temperature rise of 0.5g copper with 1W applied, if the thermal resistance of its surroundings was high it wouldn't take long to get red hot and melt. Yes there needs to be an increase in temperature first (so there's enough of a gradient for efficient/effective transfer to take place), but once this is reached, I firmly believe that most heat is dissipated through the magnet.
Also, using the time constant alone as evidence of dissipation or absorption, is only looking at one piece of the puzzle - without knowing the weight, it can't be judged how well heat transfer is taking place. And using weight + time constant is also probably a pretty convoluted way to determine the temperature of the radiator - I think you'd first need the contact area of the radiator plus the power being absorbed by the surrounding material to estimate the temperature of the radiator. Regarding contact area, if it's not direct contact, the distance between the two materials is probably required as well. IR radiation flows freely until absorbed. I believe its power dissipates like any microwave radiation. A millimeter of oxygen and nitrogen isn't much of a barrier, and the air present all has nowhere to go because behind the dome is sealed.
There's also this observation I've made:
I've seen a subwoofer, in the middle of normal loud operation, get hit with a transient that knocks its coil out of the magnetic gap. In seconds the coil was smoking. By 5, the coil was
done. The only thing that can be concluded from this is that transfer to free air is much lower than to metal with a 1-2mm buffer of air between. Much lower.
Yes, I didn't spend an inordinate amount of time finding the applicable equations to make an example with notes describing each step of the processes I described, and my last observation is completely anecdotal, but
What do you think after reading this?
edit: about woofer leads being an avenue for voice coil cooling - I've taken a spool of 50 feet of 20ga wire and put a few amps through it. The ends coming off the coil were a few degrees over ambient, while the coil itself rose by over 30 degrees. I didn't have extremely long leads, but from 2-3 inches from the coil to the ~1.5 feet to the leads (I should say foot as it was only one side - the other was connected to the inside of the roll) was the same, lower temperature.