This research will provide a new approach to the problem of managing multi-core processor thermal sensors and processing their measurements. It will rely on fundamental information theoretic principles, new problems in information theory that capture the salient features of on-chip thermal profile estimation. The associated new formulations are inspired notably by rate distortion theory and also bear a similarity to compressed sensing. Furthermore, the approach has wider applicability to general problems of parameter estimation based on limited sampled and quantized measurements. The research will improve the performance and reliability of multicore processors; and introduce new models and problem formulations in the fields of information theory and compressed sensing.