Say for example I have a sheet of metal which is 1 $m^2$. If I would heat the center of this sheet of metal to a 100 degrees celsius. How warm will a point be which is removed 10 cm from the center? How warm will a point be which 20 cm removed from the surface? and so on ... Is there an equation for this? Also, the rate of cooling does it depend on the distance from the heat source and the temperature at the heat source? (E.g. if the center is a 100 degrees, at 10 cm it is maybe 70 degrees, but if the center is 200 degrees is the temperature at 10 cm 140 degrees? So what's the relationship here?
Ok, Let me give some more info into what I want to learn, never mind the info above. I don't care if the sheet is square, round or whatever. I just want to know given that a surface/sheet is heated how does the heat spread. Let's say, we have a point (in the center of a surface for example) "$c$" which has a certain steady state temperature "$t$", how does the temperature vary with the distance from this point "$c$" ? A point "$p$" which is a certain distance removed from $c$ will be $t-\Delta t$ ... I guess. How would a 2d plot of this temperature distribution look like?
Also, if the temperature at $c$ was higher (let's say 20 degrees) ... would the temperature at $p$ also be 20 degrees higher (assume steady state) ?
I am just trying to get a better intuition into this. Feel free to point me toward relevant material or things to try out ...