Control surfaces of hypersonic vehicle in the presence of shock wave/boundary layer interaction (SWBLI) undergo time-dependent aerothermal loading. Exposure to such extreme environment makes them vulnerable to structural fatigue and premature failure. Present study focuses on assessing this fluid-thermal-structural interaction (FTSI) on a cone-slice-wedge configuration, where compliant panel mounted to the wedge acts as the control surface. Two computational frameworks based on RANS and LES are used for FTSI study backed up by high-resolution experimental data. Pressure fluctuations in boundary layer transition of a cone is computed with LES and experimentally validated. Then, FTSI of the compliant panel is predicted in the presence of laminar SWBLI. Aerothermal analysis with Reynolds Averaged Navier-Stokes (Spalart-Allmaras) reasonably predicts mean flow features but heat flux on panel surface exceed experimental measurements by 30%. A modal analysis reveals that isolated modeling of the panel could be sufficient for aerothermoelastic analysis as rest of the model is fixed as a rigid body. Generalized aerodynamic force and worksum values are computed for the first two structural mode, which indicate weakly unstable aeroelastic behavior. Frequency response solution correlates panel deformation and separation bubble oscillation. Quasi-steady FTSI for the compliant panel is computed for over half a minute and comparison with experimental data reveals excessive temperature rise owing to heat flux overprediction. Compressive thermal strains in this scenario predict static panel buckling which could not be verified with experimental data. Further, transient FSI response is computed for unheated panel and heated buckled panel. Frequency spectrum comparison with experimental data concludes absence of buckling highlighting the importance of accurately modeling aerothermal loads.