This paper presents an efficient physics-based electrothermal model that solves some advanced problems of modeling Silicon Carbide (SiC) power MOSFETs. It is the first electrothermal model that simulates the temperature dependency of the first and the third quadrant characteristics, including the reverse recovery of the body diode accurately and efficiently. It extends from a previous work that demonstrated the isothermal physicsbased model of the gate-dependent body diode. Physics-based temperature scaling of the first and third quadrant allows simulation of the self-heating effect in a wide range of temperatures (27°C -200°C), even for the synchronous operation. Moreover, a physics-based modeling approach is taken to include gate-voltage dependent non-linearity of the gate to source capacitance (Cgs). Also, a physic-based segmented cascaded method is taken to accurately model the Miller (Crss), and the output (Coss) capacitances at the low and very high drain to source voltage regions. Further, the temperature-dependent breakdown mechanism is included for reliable system design. Double Pulse Tests (DPTs) at various temperatures up to 200°C validate the model's accuracy. Lastly, a synchronous buck converter test demonstrates the model's ability to predict junction temperatures, validating the model's accuracy and efficiency in a continuous operation with self-heating.