This work explores the dynamics of a newly proposed cellular automata model, called Temporally Stochastic Cellular Automata (TSCAs), where two local rules, say f and g are applied to all cells with a probability. The first rule, say f, acts as a default rule of the system, whereas the second rule, say g, acts as a perturbation rule that perturbed the system with a probability, say \(\tau \) . This work aims to get an approach solution of a relaxed version of the Global Synchronization Problem, named the Self-synchronization Problem on TSCA. An n-cell self-synchronized TSCA reaches a homogeneous configuration ( \(0^n\)  or \(1^n\) ) from any initial configuration and oscillates between two homogeneous configurations ( \(0^n\) and \(1^n\) ) with some probability. The main focus of this work is to classify the whole set of TSCAs based on their self-synchronization capabilities.