Aluminum alloys (depending on their composition) will melt between 570 to 640 ° C (1055 to 1180 ° F). The real problem in a stove or pan is that between 150 to 200 ° C (300 to 400 ° F) aluminum and its alloys lose structural strength.. Wood camp fires can range from 550 to 1200 ° C (1000 to 2200 ° F).
Other downsides of aluminium, for wood fires, is that it conducts heat several times greater than steel or titanium, so it dissipates heat from the combustion area of the fire quickly, making it less efficient and therefore less clean burning. If used as a fire pan the high thermal conductivity of aluminum can lead to scorching the ground underneath.
Aluminum also reflects heat better than steel or titanium, which is good in focusing heat back into the burning wood, but this advantage is soon lost when soot forms on the aluminum surface from the fire. For gas stoves this high reflectivity can lead to over heating of the gas canister. The flip side of reflectivity is emissivity. While steel emits heat 4 times more than aluminum, the much greater conductivity of aluminum negates this effect.
The specific heat capacity of aluminum is twice that of steel and titanium so the metal takes twice as long to heat up or cool down. Factoring this in with the other chemical and mechanical properties, nobody would use aluminum for stoves, windscreens or pans if it was not so light and low cost. And, If it was not for the fact that when cooking water in the food keeps the pan temperatures down to 100 ° C (212 ° F) we could not use aluminum for cooking when any structural strength is required.
Sorry, it is the nerd in me.