Cooling rate of isolated heat source

This is probably an easy question but i need to estimate the time required for a localized hot spot on the surface of mica to dissipate the excess energy and return to room temperature. There is no forced cooling, i.e. cooling only by ambient air and phonons.
Let
T1 =100C (Hot Spot max temp)
T2 = 23C (Final temp)
Hot spot area ~0.5 micron^2

Thanks in advance
jh

 

One important consideration is the volume of mica that needs to be cooled. What is the thickness of this mica? Also, can the heat dissipate through the mica to the surroundings? I think it would, but is there a reason why you assume it does not?

 

I should clarify myself. The "surrounding" that I was talking about was the surrounding mica. In other words, heat can transfer through the mica to the surrounding mica. Also, heat transfer will occur by natural convection to the air.

The Fourier number and the Biot number need to be calculated to determine the approximate time. The product superposition principle (I think) can be used for your problem if you assume the initial temperature of the surrounding mica is 23C.