AFAIK Aluminum wires will become a heat liability, especially at higher amps

That's why my calculation example used a 1.5mm2 copper wire but a 2.4mm2 aluminum one.

Aluminum has a higher resistance, which means the same diameter will get hotter than copper. Make the cable thicker and its resistance drops, which means it gets less hot.

Want more amps at the same temperature? Ohm's law still applies: just use a thicker cable.

Any wire---of any non superconducting material---will be hotter at higher current flows. You size the wire to the application.

It depends on design, environment and maintenance. If it's well protected against oxidation and it's static, it's not really a problem. Heat issues are often at the joints, which are most vulnerable, but can be coated and encapsulated to mitigate. For some uses, aluminium is superior to copper all things considered. Obviously the diameter of the wire/cable depends on which conductor you use, AC/DC, current and service temp - for some applications, that may favour one material over the other.

If the two wires are the same gauge, yes. If you size up the aluminum, at the same resistance/current would mean the same amount of power over the length of the conductor and same heat.

Thicker cables or higher voltage(lower current) is the answer which is why it's used in power distribution networks where they can control the voltage by planning what to transform to.