Thankyou all for providing a direction to go ahead. will try some methods or simulations and see if it can be predicted as close as possible to the experimental results. @Steve4Physics Yes, it is a homework, practical project which has high complexity.
Thankyou @Steve4Physics for noticing the max current limitation with respect to the wire gauge. Yes, it is a practical homework, trying to figure out if we can develop a mathematical relation between the time vs temperature for constant power applied.
Also, mentioned above have tried to...