Colloidal quantum dots (QDs), which consist of inorganic cores surrounded by soft organic ligands, can self-assemble into superlattices exhibiting long-range order. Their tunability, in terms of size, shape, and ligand properties, makes them promising for applications in solar cells, photodetectors, and light-emitting diodes. However, the complex interplay between ligand stiffness, QDs cores-ligands coupling strength, and its impact on QDs' morphology and thermal properties is not well understood. This work employs molecular dynamics simulations to investigate the possibility of modulating the thermal conductivity of QDs superlattices via ligand engineering. It is found that the structural stability of QDs superlattices depends significantly on the interaction strength between the QDs cores and ligands. At lower interaction strengths, the instability manifests itself in a random fusion of the QDs cores, while at intermediate strengths a stable simple cubic lattice structure is maintained. Higher interaction strengths lead to amorphization in the surface regions of QDs core. We observed a nonlinear trend in the thermal conductivity with varying QD-ligand interaction strengths due to competing factors: fusion of QDs cores at lower interaction strengths and increased crosslinking interaction among ligands at higher interaction strengths. The influence of ligand stiffness on thermal conductivity was found to be minimal. This study provides a deep insight into the role of ligand stiffness and interaction strength on structural dynamics and thermal transport in QDs superlattice and demonstrates the feasibility of engineering thermal transport in QDs superlattice via ligand engineering.