Compared with line-commutated converter-based high-voltage direct current (LCC-HVDC) transmission, flexible modular multilevel converter-based high-voltage direct current (MMC-HVDC) transmission offers advantages including independent control of active and reactive power, rapid response, and low harmonic content, allowing it to play an increasingly significant role in DC transmission systems. As a fundamental device of a flexible DC converter valve, the insulated gate bipolar transistor (IGBT) is recognized for its rapid switching capabilities and straightforward drive requirements. IGBT losses mainly include conduction and switching losses. Using the thermal resistance parameters of the device and its heat sink, the junction temperature under steady-state conditions can be calculated; however, determining the transient thermal impedance under overload conditions remains challenging. Therefore, analyzing the junction temperature under overload conditions has become a technical hurdle. To calculate the junction temperature at the IGBT slug, this study employs the electrical topology of a flexible DC converter valve and establishes a Cauer thermal network model of the corresponding IGBT, developed based on the theory of thermoelectricity analogy. Then, it has obtained the junction temperature in the time domain through the Laplace transform and the inverse Laplace transform. This approach has overcome the difficulty of calculating the junction temperature of an IGBT under overload conditions. Additionally, the electro-thermal coupling simulation is conducted in COMSOL to investigate the junction temperature characteristics of the device when the flexible DC converter valve operates under twice the rated load.