This paper addresses the problem of chip level thermal profile estimation using runtime temperature sensor readings. We address the challenges of a) availability of only a few thermal sensors with constrained locations (sensors cannot be placed just anywhere) b) random on-chip power density characteristics due to unpredictable workloads and fabrication variability. Firstly we model the random power density as a probability density function. Given this random characteristic and runtime thermal sensor readings, we exploit the correlation between power dissipation of different chip modules to estimate the expected value of temperature at each chip location. Our methods are optimal if the underlying power density has Gaussian nature. We also present a heuristic to generate the chip level thermal profile estimates when the underlying randomness is non-Gaussian. Experimental results indicate that our method generates highly accurate thermal profile estimates of the entire chip at runtime using only a few thermal sensors.