Coupled Map Lattice systems have been extensively studied in the past. The behavior of such systems under various mechanisms for the suppression of chaos has been investigated. The suppression of chaos is investigated here for both spatial as well as temporal variations of parameters. For this, the well-known Logistic map is used as the dynamical system. The method of homogeneous pinning is used as the chaos suppression mechanism. It is found that with pinning conditions, the STC when (i) control parameter r having only spatial variation together with coupling parameter ϵ having either only temporal temporal variation or spatial as well as temporal variation at the same time, (ii) r having temporal variation with every possible variation in ϵ and (iii) r having both spatial as well as temporal variation at the same time with every possible variation in ϵ, appears to have narrow range of values with non-suppression of chaos. However, upon close examination, it is found that the system is not chaotic at all.