Abstract Racetrack coils in REBCO High-Temperature Superconductor (HTS) motors help to increase the power-over-weight ratio by raising the magnetic flux density and output power. Nevertheless, HTS motors face thermal quench due to self-heating effects when subjected to alternating or short-circuit onset DC voltage. Additionally, thermal events have been observed due to screening currents when motors operate at high frequencies. Therefore, for the safe operation of HTS motors, quench research is crucial. To accurately simulate and analyze quench events in different scenarios, it is imperative to employ fast and precise software to numerically model the electrothermal behavior in racetrack coils. Our contribution involves the development of a novel and efficient model implemented in C++ that takes screening currents into account. This model is designed to conduct coupled electromagnetic and electrothermal analyses, utilizing variational methods. Specifically, the model incorporates both Minimum Electro-Magnetic Entropy Production and the Finite Difference Method. In this article, we explore the phenomenon of temperature rise within a racetrack coil subjected to either alternating or DC voltages of magnitudes ranging from 0.1 V to 1000 V. The study encompasses conditions of adiabatic operation and heat exchange with liquid nitrogen (LN2). Among other results, we found that in moderate DC voltages like 10 V, non-uniformity in the AC loss causes highly localized quench at the central turns. Then, screening currents play a key role also for DC voltages. The developed model exhibits the potential to comprehensively and swiftly analyze the electromagnetic and electrothermal characteristics of real-world superconducting applications, including high-field rotating machines, such as motors for aviation.