Max Temperature Peak: Global vs Local Energy Source

[porcupine6789]

Ok, so say I have a system at a global temperature, I add an energy source (laser in this case) and it heats the system in a localized area. This leads to a maximum temperature peak in the system. Then you can get out a change in temperature from this maximum to the global. OK, now my question is say in increase the global temperature and keep the power source the same, would I expect to find the delta temperature to be the same for small global temperatures, or would I expect to find that the change from global to max is greater when the global temperature is greater. Hopefully that made some sort of sense.

 

[alxm]

If you don't mind me rephrasing it, I think you're asking:
"Does adding a given amount of heat to a system always raise the temperature by the same amount? (Locally before equilibration and globally after it's equilibrated)"

The answer would be no. The heat capacity (change of temperature per unit of heat energy) is not usually constant with temperature, nor is the heat conductivity (which together with the heat capacity would determine the maximum temperature peak during heating).