To solve this problem we can apply the concept related to thermal expansion, including the analogy with resistance and final intensity.
The mathematical expression that describes the expansion of a material by a thermal process is given by
[tex]R = R_0\alpha \Delta T[/tex]
Where
[tex]R_0[/tex]= Initial resistance
[tex]\alpha =[/tex] Thermal expansion coefficient
[tex]\Delta T =[/tex] Change in the temperature
If we want to directly obtain the final value of the resistance of the object, you would simply add the initial resistance to this equation - because at this moment we have the result of how much resistance changed, but not of its final resistance - So,
[tex]R_f = R_0 + L_0\alpha \Delta T[/tex]
[tex]R_f = R_0(1 + \alpha \Delta T)[/tex]
Re-arrange to find the change at the temperature,
[tex]\Delta T=\frac{1}{\alpha}\frac{R_f}{R_0}-1}[/tex]
Since the resistance is inversely proportional to the current and considering that the voltage is constant then
[tex]R \propto \frac{1}{I}[/tex]
Then,
[tex]\Delta T=\frac{1}{\alpha}\frac{I_0}{I_f}-1}[/tex]
[tex]\Delta T = \frac{1}{4.5*10^{-3}}(\frac{I_0}{I_0/8}-1)[/tex]
[tex]\Delta T = \frac{1}{4.5*10^{-3}}(8-1)[/tex]
[tex]\Delta T = 1555.5k[/tex]
(It is possible that there is a typing error and the value is not 4.5 but 4.3, so the closest approximate result would be 1627K and mark this as the correct answer)
