This document discusses the design and analysis of a thermal model for induction motor protection. It begins by explaining the limitations of traditional overcurrent relays in providing adequate thermal protection for motors. It then derives a first-order thermal model based on the motor's thermal limit curves. The model treats the motor as a heated homogeneous body and derives differential equations relating temperature rise, heating power, and thermal losses. It establishes equivalences between the thermal model and an RC circuit. The document also describes how to fit the model's equations to the manufacturer-provided thermal limit curves and establishes a correlation between motor temperature and current levels. The goal is to implement this thermal model in numerical relays to continuously monitor motor temperature in real-time and initiate a