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.

Aluminum has lower resistance per kg, or per $. This is why transmission lines use aluminum (around a steel core).