Hot extrusion involves heating a metal above its recrystallization temperature to make it easier to deform plastically. For aluminium, this temperature typically falls in the range of:
\[
0.6T_m \text{ to } 0.75T_m \quad (\text{in Kelvin}),
\]
where \( T_m \) for aluminium is approximately \( 933 \, \text{K} \) (or \( 660^\circ \text{C} \)).
\[
0.6 \times 933 \approx 560 \, \text{K} \quad \text{and} \quad 0.75 \times 933 \approx 700 \, \text{K}
\Rightarrow \text{in } ^\circ\text{C}: \quad 287^\circ \text{C} \text{ to } 427^\circ \text{C}
\]
Hence, \( 350^\circ \text{C} - 500^\circ \text{C} \) falls within the safe range used for hot extrusion of aluminium, allowing sufficient ductility and reducing the extrusion pressure.