A study of thermal behavior for two-dimensional spin-crossover compounds is performed by using an Ising-like model including both short-range and long-range interactions and a Monte Carlo entropic sampling technique for determining the associated density of states. The effects of various factors, such as external pressure, internal interaction strength or system size, on the thermal transition are analyzed and compared to several experimental findings in this area. The study is focused on two-step transitions and the conditions for hysteresis behavior at each step which are especially important for the potential applications of spin-crossover materials in data storage devices or smart sensors.