I’d done this check before and I just made a spreadsheet with the thermal conductivities and densities of Aluminum, Copper, Brass, Silver, Gold, Iron, and Titanium and their common alloys.
The heat transfer per weight (in units I’m not going to bother to figure out) are best for
Aluminum: 88
Copper: 44
Silver: 40
Gold: 16
Brass: 15
Iron: 9
Titanium: 5
So, if you were born with a silver spoon in your mouth, you, Mr. Trump, might want to go ahead and use it. But if you have to buy the silver spoon, or steal it from your wife, copper is better per weight and a LOT better per cost.
Aluminum seems to be better per weight by a factor of 2, and it is, until you make aluminum oxide. Aluminum oxide is crap at conducting heat. And eventually, you’ll erode all the aluminum away as the aluminum oxide erodes away.
I don’t have to solve the differential equations to know that if I can take my conductor higher in temperature at the hot end, that everything is better. With aluminum, I must keep the tip out the direct flame or accept a high erosion/corrosion rate. With copper, I can take the tip to a much higher temperature – potentially twice as much – and a correspondingly higher rate of heat transfer.
Conclusion: in ambient temperature applications, the higher conductivity, low weight, and lower cost of aluminum make it preferable. You see it used on computer chips (100-300F), heat fins in a hydronic baseboard (160-200F), and, increasingly, in car radiators (180-240F). You don’t see it used in flames. Copper, although 2nd place in conductivity per weight, lets you go to a higher temperature. Also, it’s trivial to solder copper bits together (I’ve literally done it with a camp stove) but a lot harder to MIG or TIG weld aluminum.