If impedance were a factor your air conditioner would not work. Look, a hot tank can be dipped in 75F sea water for one minute and the tank pressure will drop 300 psi. If that doesn't convince you nothing will.
These theoreticians seem to forget that 35 pounds of steel or aluminum hold a lot more heat than 6 pounds of air. When that metal touches water, heat is going to move on and out, FAST. It will move faster with aluminum because of its conductivity. However, the steel tank usually starts out hotter so it is a close call since heat transfer depends on temperature differences. Also, it should be noted that total heat capacity is a function of mass, and that steel and aluminum tanks have about the same mass contrary to what you have been told. However, I seem to recall that capactance per unit mass is higher for aluminum but I would have to check that. I don't really care. Divers know that aluminum will cool faster than steel.
When that happens heat is pulled from the air inside at a rapid rate. This process is helped by convection currents inside the tank. It happens rapidly, especially with aluminum but don't hasten to pull the tank out of the water immediately. The tank will warm up if it is pulled from the water too fast. This is due to the fact that the metal is still capturing heat from the air inside the tank.
It is true that I have done a substantial amount of theoretical heat transfer calculations during the last 30 years, but many (if not most) of my calculations have been confirmed with some kind of real experiment…some times very precise experiments, other times with just physical observations.
As I mentioned above one of the assumptions was that the water and tanks start at room temperature. A very quick hot fill was then performed. I did not analyze the heating cycle, just the cooling cycle since that is where the cooling water comes into play. This and all the other assumptions where selected as being reasonable condition.
Also the calculation uses the lumped mass transient heat transfer assumption… both the actual mass and thermal capacitance of the air and the metal are taken into account.
To make the calculations reasonably simple (after all, I did this just for the fun of it) I took some simplifying assumptions that IMHO are very reasonable.
I have not done any precise experiments to back these calculations, but it does seem to agree with my real life observations filling tanks.
There is nothing magic about heat transfer calculations, if you would like I will be glad to email you a copy of my Excel spread sheets.
BTW, thermal impedance is just the heat transfer term for the inverse of conductance. It is sort of parallel to resistance and conductivity in an electrical circuit.
The thermal impedance (or conductance) of any solid substance is calculated based on its thermal conduction coefficient, the heat flow area and distance heat has to travel in the geometry being analyzed. For a fluid it involves the convection coefficient and the interface area from the fluid to adjacent solid.
I highlighted part of your statement that confirms my calculations. I just tried to put some reasonable numbers behind those observations…like I said; you are welcome to review my calculations.