The amount of heat produced in a wire depends on its

(a) Thickness

(b) Material

(c) Length

Amount of heat produced in the wire, H = ${\mathrm{I}}^2\mathrm{Rt}$

where, 

R = resistance of wire.

I = Current through the wire.

t = time

As the resistance of the wire $\mathrm{R} \mathrm{\alpha } \frac{\mathrm{L}}{\mathrm{A}}$

So, the heat produced depends on length, thickness (cross-section area), and material.