We propose a fast thermal modeling tool using a Green's function based approach. Green's function based 
approaches have been shown to be faster than the traditional finite difference based techniques. Our 
proposed tool can model steady state and transient thermal profiles for both 2D and 3D chips, which may 
contain multiple active layers and fluid carrying microchannels for heat removal. The most unique advantage 
of our tool is that it models leakage power analytically using a piece-wise linear leakage model, thereby 
eliminating the need to iterate multiple times through the leakage-temperature feedback loop. 
We use several algebraic techniques and transforms to compute the thermal profile analytically and to 
speed up the temperature calculation. Our approach provides a 60X speedup over state of the art thermal 
simulators, with an error limited to 5%.