High-voltage dry-type DC-link capacitor is a critical component of the multi-level converter for flexible DC transmission, serving as an energy storage element in the sub-module and performing functions such as voltage support and harmonic filtering in the circuit. Thermal stability is a pivotal factor in ensuring the reliable operation of high-voltage dry-type DC-link capacitors under overload conditions. This paper undertakes a comprehensive analysis of the operating conditions of high-voltage dry-type DC-link capacitors. It first extracts the main operating voltage characteristic parameters and then carries out research on the thermal stability test method of DC-link capacitors in combination with their structural characteristics. Based on the test method stipulated in IEC 61071:2017, the thermal stability test of DC support capacitor under pure AC voltage is carried out, and then the thermal stability test circuit of DC support capacitor with DC superimposed on AC voltage is constructed to carry out the thermal stability test of DC support capacitor under close to the actual operating conditions. The results obtained from this process are then analyzed, leading to the thermal stability test method that is applicable to high-voltage DC-link capacitors.