The present work explores new approaches regarding fluid-structure interaction using supercritical CO2. The main objective is to combine the Lattice Boltzmann methods(LBM) with a cubic equation of state that allows the properties of supercritical CO2 to be correctly represented. Although the LBM theoretically allows the resolution of the energy conservation equation,the computational cost to carry out the simulations is high [1]. Therefore, recent studies have been carried out to increase the capabilities of the method at a low computational cost, using segregated methods. From this perspective, double probability function methods and hybrid methods exist. The latter present better stability compared to the former. However, the vast majority of these works represent the fluid as an ideal gas, in which the equations of state are convex and do not capture the behavior of a real gas. For the correct simulation of CO2 in the supercritical state, it is necessary to determine its thermodynamic properties precisely, and this can be solved using cubic equations of state, such as the Peng-Robinson equation. Therefore, the present work aims to perform a coupling between these models and a cubic equation of state to have a better representation of supercritical CO2 flow. Additionally, fluid-structure interaction methods are explored, such as the immersed boundary method, in order to represent a solid in a supercritical CO2 flow. This model is validated through different academic cases such as a sod Tube, Thermal Couette Flow, Thermal Poiseuille flow among other test cases.