In recent years, Kitaev materials have garnered significant attention for their unique physical properties. While light-field manipulation of magnonic topological states in realistic two-dimensional ferromagnetic systems has been extensively explored theoretically, existing studies remain largely confined to zero-temperature or static limits. Consequently, several critical issues remain unresolved: the dynamic mechanisms of magnonic gap closing and reopening in light-driven ferromagnets at finite temperatures below the Curie point; the quantitative validation of thermal Hall conductivity as a criterion for topological phase transitions; and the differential impacts of light irradiation on the critical points of temperature- versus magnetic-field-induced topological phase transitions. To address these challenges, we develop a self-consistent renormalized spin-wave theory within the mean-field approximation for a two-dimensional honeycomb Kitaev-Heisenberg ferromagnet with Dzyaloshinskii-Moriya interaction. We systematically investigate the renormalization effects arising from magnon-magnon interactions under laser irradiation. Our key findings are threefold. First, we reveal a reversible, light-controlled magnonic bandgap tuning mechanism at finite temperatures. We demonstrate that, under specific light intensities and below the Curie temperature, the magnonic bandgap can be closed and reopened solely by adjusting temperature or magnetic field. This finding overcomes the limitations of previous studies restricted to zero-temperature photoinduced topological phase transitions. Second, we establish the sign reversal of thermal Hall conductivity as a reliable experimental signature of topological phase transitions. Numerical calculations of the Chern numbers across the critical point confirm that the topological phase transition is characterized by magnonic bandgap closure at the Dirac point within the thermodynamically stable region. Crucially, the jump in the Chern number strictly corresponds to the anomalous variation in thermal Hall conductivity.Third, we uncover a novel asymmetric evolution of the topological phase diagram induced by light irradiation. Increasing light intensity synchronously reduces both the critical temperature (T_c) for temperature-induced topological phase transitions and the Curie temperature, while significantly increasing the critical magnetic field (h_c), for magnetic-field-induced transitions. This previously unreported asymmetry elucidates the distinct influence mechanisms of temperature and magnetic field on band structures under varying light intensities and provides new insights into the selective control of topological phase transition pathways via light fields. Notably, the accompanying sign reversal of thermal Hall conductivity serves as a vital indicator for the experimental detection of these topological phase transitions.