We report the tunable temperature dependence of Mn luminescence spectral characteristics (peak position and bandwidth) in Mn-doped CdS/ZnS core/shell nanocrystals via controlled local lattice strain at the dopant site that affects the local vibronic coupling and local thermal expansion. The lattice mismatch at the core/shell interface creates a gradient of lattice strain in the shell along the radial direction that allows varying the local lattice strain at the Mn2+ site via the controlled radial doping location. Increasing the local lattice strain at the Mn2+ site results in the stronger temperature broadening of Mn luminescence bandwidth due to the increasing softening of the vibrational mode coupled to Mn2+ ligand field transition. Larger local lattice strain also causes a stronger temperature dependence of the luminescence peak, which indicates the enhanced local thermal expansion at the dopant site.