Experimental investigations of fuel droplet evaporation and combustion commonly rely on a solid fiber to suspend the droplet. In numerical simulations, however, the thermal influence of the fiber is often neglected or accounted for through simplified correlations within one-dimensional models. In this work, we relax these assumptions by employing an interface-resolved multiphase CFD framework that explicitly accounts for conjugate heat transfer between the gas–liquid system and the solid fiber. The present study builds upon a VOF-based multicomponent evaporation model, previously extended to a low-Mach-number, variable-property formulation and to include detailed combustion chemistry. In earlier developments, the solid fiber was treated solely as a geometrical entity to suspend the droplet via surface tension. Here, we extend the model by solving the energy equation within the solid fiber and by fully coupling heat transfer at the fluid–solid interface. The model is employed to quantify the impact of the suspending fiber on droplet consumption dynamics under both evaporation and combustion conditions, in microgravity and normal-gravity environments. The results show that the presence of the fiber breaks the spherical symmetry typically observed in microgravity simulations, locally quenches the flame, and provides an additional heat transfer pathway between the external environment and the droplet. These effects can have a significant influence on the droplet lifetime, depending on the fiber material and characteristic dimensions. The proposed model proves capable of explaining discrepancies reported in the literature between experimental and numerical results, guiding experimental design, and identifying the regimes in which the thermal effects of the suspending fiber cannot be neglected. Future work will focus on extending the framework to different fiber geometries (e.g., rod-like supports) and on investigating the interplay between conjugate heat transfer and Marangoni-driven convection.