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Dynamic thermal management techniques require accurate runtime temperature information in order to operate effectively and efficiently. In this paper, we propose two novel solutions for accurate sensing of on-chip temperature. Our first technique is used at design time for sensor allocation and placement to minimize the number of sensors while maintaining the desired accuracy. The experimental results show that this technique can improve the efficiency and accuracy of sensor allocation and placement compared to previous work and can reduce the number of required thermal sensors by about 16% on average. Secondly, we propose indirect temperature sensing to accurately estimate the temperature at arbitrary locations on the die based on the noisy temperature readings from a limited number of sensors which are located further away from the locations of interest. Our runtime technique for temperature estimation reduces the standard deviation and maximum value of temperature estimation errors by an order of magnitude.