Résumé : We study thermal transport along the edge of a small chiral spin liquid device coupled to two Ising-chain reservoirs, a platform suitable for quantum-engineered systems. Adiabatically switching on the tunnel couplings to the reservoirs generates a thermal current that dynamically builds up and reaches a quasi-steady-state regime. In this experimentally critical time window, the two-terminal thermal conductance can approach half-quantized values—a hallmark of Majorana-mediated transport—under finely tuned conditions. The results agree with an effective Landauer-Büttiker description in the large-reservoir limit, where energy-resolved transmission rates help identify the optimal parameters to achieve the half-quantized conductance. This work provides a controllable platform to investigate topological thermal transport in engineered spin systems, such as realized in cold-atom and Rydberg-atom settings.