This study numerically investigates unsteady mixed convection and fluid–structure interaction in a two-dimensional open cavity containing an internal adiabatic circular cylinder. Three configurations are examined to evaluate the thermo-hydrodynamic effects of structural compliance: a flexible fin attached to the lower side of the cylinder, an oscillating elastic upper wall, and the simultaneous use of both compliant elements. The flexible fin is subjected to a harmonic tip force, whereas the elastic wall is driven by a distributed oscillatory load. The influences of excitation frequency, Young’s modulus, and fin length are assessed in terms of instantaneous and time-averaged Nusselt number, pressure-drop coefficient, local heat transfer, and thermal performance ratio. The results show that both the flexible fin and the elastic wall significantly alter the cavity recirculation structure, intensify fluid mixing, and periodically disturb the thermal boundary layer over the heated wall. For the fin-only configuration, heat transfer enhancement strongly depends on fin stiffness, length, and excitation frequency, with intermediate stiffness and larger fin length generally producing superior thermal performance. For the elastic-wall-only configuration, wall oscillation increases the mean Nusselt number relative to the rigid-wall case, although excessive excitation frequency results in a substantial increase in hydraulic resistance. Among all examined cases, the combined flexible-fin/elastic-wall configuration produced the highest time-averaged Nusselt number, with an enhancement of nearly 28% relative to the fully rigid reference case. Overall, the simultaneous application of the flexible fin and the elastic wall is shown to be an effective strategy for enhancing convective heat transfer in open-cavity systems.