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In this work, we present a novel approach to real-time tracking of full-chip heatmaps for commercial off-the-shelf microprocessors based on machine-learning. The proposed post-silicon approach, named RealMaps, only uses the existing embedded temperature sensors and workload-independent utilization information, which are available in real-time. Moreover, RealMaps does not require any knowledge of the proprietary design details or manufacturing process-specific information of the chip. Consequently, the methods presented in this work can be implemented by either the original chip manufacturer or a third party alike, and is aimed at supplementing, rather than substituting, the temperature data sensed from the existing embedded sensors. The new approach starts with offline acquisition of accurate spatial and temporal heatmaps using an infrared thermal imaging setup while nominal working conditions are maintained on the chip. To build the dynamic thermal model, a temporal-aware long-short-term-memory (LSTM) neutral network is trained with system-level features such as chip frequency, instruction counts, and other high-level performance metrics as inputs. Instead of a pixel-wise heatmap estimation, we perform 2D spatial discrete cosine transformation (DCT) on the heatmaps so that they can be expressed with just a few dominant DCT coefficients. This allows for the model to be built to estimate just the dominant spatial features of the 2D heatmaps, rather than the entire heatmap images, making it significantly more efficient. Experimental results from two commercial chips show that RealMaps can estimate the full-chip heatmaps with 0.9C and 1.2C root-mean-square-error respectively and take only 0.4ms for each inference which suits well for real-time use. Compared to the state of the art pre-silicon approach, RealMaps shows similar accuracy, but with much less computational cost.