In this paper, we propose the design of an ultra-fast temperature simulator (LightSim) that can perform both steady state and transient thermal analysis, and also take the effect of leakage power into account. We use a novel Hankel transform based technique to derive a transient version of the Green's function for a chip, which takes into account the feedback loop between temperature and leakage. Subsequently, we calculate the temperature map of a chip by convolving the derived Green's function with the power map. Our simulator is at least 3500 times faster than HotSpot, and at least 2.3 times faster than competing research prototypes [4, 12]. The total error is limited to 0.18 °C.