Formula to calculate heating time of nichrome?
here is a hint

Silicon (not nichrome) has thermal capacity of 1.6 picoJoules per cubic micron per degree Centigrade. When you short the output of a modern MCU, or logic gate such as 74HCT00, you will very rapidly heat the internal FETs, perhaps to destruction. The numerous thermal paths are not able to remove the heat fast enough, and the tiny transistors self-destruct.

If your energy input to your nichrome is very high, then the AIR and the MOUNTING CLAMPS will not matter.

In that case, all you care about is the volume of the "wire", its total specific heat, and the rate of energy input.