Heat generation rate to temperature
To find the temperature rise you will need to analyze the heat loss vs. temperature by all methods (typically conduction, radiation and convection). 

Conduction can often be approximated as a simple linear relationship for a fixed geometry (like Ohm's law). Radiation loss is very nonlinear (proportional to the difference of the 4th power of the absolute temperatures) and convection is.. complex.. with different types of fluid flow possible under different conditions. 

It's possible to use programs such as COMSOL or NASTRAN to analyze the effects, but quite a bit of work will be necessary to model the situation if you want the result to resemble reality.