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With the scaling up of transistor densities, the thermal management of integrated circuits (IC) in 3D designs is becoming challenging. Conventional simulation methods, such as finite element methods, are accurate but computationally expensive. Compact thermal models (CTMs) provide an effective alternative and produce accurate thermal simulations using numerical solvers. Recent work has also designed machine learning (ML) models for predicting thermal maps. However, most of these ML models are limited by the need for a large dataset to train and a long training time for large chip designs. To overcome these challenges, we present a novel ML framework that integrates with CTMs to accelerate thermal simulations without the need for large datasets. We introduce a methodology that effectively combines the accuracy of CTMs with the efficiency of ML using a physically informed linear regression model based on the thermal conduction equation. We further introduce a window-based model reduction technique for scalability across a range of grid sizes and system architectures by reducing computational overhead without sacrificing accuracy. Unlike most of the existing ML methods for temperature prediction, our model adapts to changes in floorplans and architectures with minimum retraining. Experimental results show that our method achieves up to 70x speedup over the state-of-the-art thermal simulators and enables real-time, high-resolution thermal simulations on different IC designs from 2D to 3D.