We study the thermal evolution of three types of quantum correlations under the homogeneous and inhomogeneous spin star Hamiltonian. It is shown that quantum discord is more stable than the other measures in the thermal regime, but Concurrence is more efficient when the Hamiltonian parameters are employed. However, all quantum correlations can reach their maximum, if the inhomogeneous parameter raises. Quantum correlations can be enhanced by a weak external magnetic field and strong coupling parameter. But they vanish in the case of a strong magnetic field, weak coupling parameter, and high temperatures.