Indium plays a significant role in chalcogen-based glasses and glass ceramics due to its unique properties that make it useful in the development of these glasses. In the current study, thermal analysis was carried out to investigate the kinematics of glass transition and crystallization in the recently synthesized alloys of the STSI system. In this system, Indium (In) is included as a modifier foreign impurity to see its impact on the kinetics of glass transition and crystallization. The calorimetric experiments with adequate precision have been performed in the differential scanning calorimetry (DSC) to obtain the DSC thermograms at different heating ramps. The complete set of different kinetic parameters has been computed for the deep thermal analysis of the kinematics. The compositional variations of the glass transition/crystallization temperatures (i.e., Tg and Tc) and the corresponding activation energies (i.e., Eg and Ec), thermal stability (i.e., Saad-Poulin S parameter and peak values of rate constant Kp) and tendency of glass formation (i.e., Hruby parameter Hr) have also been discussed in details.