The aim of the paper is to present the results of the investigation of the thermal conditions (temperature distribution, heat losses) in the support system of the vapor suppression tank (VST) of the vacuum vessel pressure suppression system (VVPSS), a safety important system of ITER fusion reactor, protecting the vacuum vessel (VV) against overpressures. The VVPSS includes four VSTs of identical volume and installed as two stacked assemblies. The study focuses on the optimization of the design of the thermal insulation at the bottom of the VSTs, interfacing with the basement and also on the identification of the thermal loads at the interface between the tank support and the tank pressure boundary. A computational fluid dynamics (CFD) analysis of the VST has been performed for four different insulation configurations and considering both steady-state and transient loads following accidental conditions. The results of the analysis are used to provide recommendation on the optimum configuration of the thermal insulation. Measures for minimization of the thermal gradient in the critical area of the joint between the tank hemispherical head and support skirt to limit the thermal fatigue on the welds are also suggested.