A simplified model of the star-branched and linear polymers was studied by the means of the computer simulations. The model chains were built on a simple cubic lattice forming star-branched polymers consisting of f = 3 arms of equal lengths. The simulations were carried out in a wide range of temperatures-from a random coil to a collapsed globule regime. The replica exchange Monte Carlo method was used for calculation of properties of the model system. The detailed comparison of this new method with the classical Metropolis scheme, which uses simulated annealing. It was shown that the Metropolis algorithm is correct for high temperatures. In the transition region and below the transition temperature the results obtained by the two methods differ significantly. The replica exchange technique finds lower energy states than the other method. The temperature of the coil-globule transition calculated using the RE algorithm is usually slightly shifted toward lower temperatures. The differences increase moderately with length of the chain and with its stiffness. The features of the transition do not depend on the simulation method although it is more rapid for the replica exchange simulations.