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Embedded temperature sensors based on proportional-to-the-absolute-temperature (PTAT) current sources have the potential to lay the foundation for low-cost temperature-aware integrated circuit architectures if they meet the requirements of miniaturization, fabrication process match, and precise estimation in a wide range of temperatures. This paper addresses an analytical approach to the minimum-element PTAT circuit design capitalizing on the physics-based modeling of the heterojunction bipolar transistor (HBT) structures. It is shown that a PTAT circuit can be implemented on only two core HBT elements with good accuracy. Derived parametric relations allow a straightforward specification of the thermal gain at the design stage, which affects sensor sensitivity. Further derived current-to-temperature mapping expresses a temperature estimate based on the measured PTAT output current. Numerical examples indicate attainable estimation accuracy of 0.43% in case of a measurement instance taken in the absence of measurement noise.