The lattice model for a star-shaped polymer with a total number of up to 72 segments is considered. The number of arms varied, ranging from 2 to 6. Entropic sampling Monte Carlo simulation is used to obtain the equilibrium, thermal and structural properties of the considered systems over a wide range of temperatures. The coil-globule transition is observed and the transition temperature is shown to shift toward lower temperatures with an increase in the number of arms. This study demonstrates how the structure of the star-shaped polymer affects its equilibrium properties.