The thermodynamic characteristics and magnetic properties of monoaxial chiral helimagnet have been investigated by using a combination of ab initio calculations and classical Monte Carlo simulations. Ab initio calculations make it possible to calculate the values of magnetic moments and exchange coupling parameters for crystal structure CrNb3S6 which show the presence of the antiferromagnetic nature of the interaction for magnetic Cr atoms. The Monte Carlo simulations with ab initio exchange coupling constants as input parameters allow us to calculated thermodynamic characteristics such as magnetization, heat capacity, and susceptibility. Calculated values of heat capacity and susceptibility make it possible to determine the phase transition temperature from paramagnetic to antiferromagnetic phase. The crossover to chiral soliton lattice in monoaxial chiral helimagnet is determined by the temperature dependence of magnetization under various external magnetic fields.