An interesting model for spin crossover compounds (SCC) is the so-called spin-phonon coupling model. In this model, the SC units are linked by springs, with elastic constants dependent on their spin states. In the present work, we investigate by means of Monte Carlo Metropolis method, the one-dimensional version of the model at T > 0 K. The relevance of our numerical analysis stands in the possibility of studying this model in the general case, i.e., outside the analytical limits of the mean-field approximation (MFA). First, we investigate a couple of model properties, such as pressure-induced-like effects on thermal hysteresis loops, system size and degeneracy influences on the dynamic phase diagrams. We find a high sensitivity of the hysteresis loops on the system size for small sizes only. Second, we qualitatively compare our results with those analytically obtained in the MFA and determine the limits of the latter. Third, we study the kinetic effects on the dynamic phase diagrams and the critical temperature. We find a slow asymptotic decrease of the critical temperature T c to zero as the kinetics becomes infinitely long. This might be important in the experimental studies of pressure-induced phase transitions for clusters or nanosize SC compounds at low temperatures, as this means that, in practice, there will always be a pseudophase transition, as the measurement time is finite. The transition temperatures are smaller than 0.1 /k B , meaning that is not a question of thermal activation, but it is really the mechanism of spin-phonon coupling that helps the transition from the low-spin to the high-spin level state.