In this study, we performed Monte Carlo coupled multi-physics simulations with spatially continuous material properties via Functional Expansion Tally combined with delta-tracking. The proposed multi-physics coupling framework significantly reduces the need for spatial discretization in the problem geometry, potentially decreasing simulation time as macroscopic cross section reconstructions are performed less frequently. The proposed method has been tested on pin-cell and assembly levels at hot full power to evaluate its applicability. At both pin and assembly levels, numerical experiments have demonstrated that the proposed framework can produce solutions that asymptotically approach those from conventional cell-based discretized simulations with infinitesimal cells. Furthermore, the proposed method accelerates the simulation time by over four times compared to the cell-based discretized approach with very small cells for cases without neutron absorbers. Therefore, the proposed method has the potential to be integrated into future Monte Carlo production codes, to meet the demanding requirements for improved reactor safety.