  A spin star system consisting of three peripheral two-state systems and a
central one is considered, with the peripheral spins assumed to interact with
each other, as well as with the central one. It is shown that such two
couplings, each one being a thermal entanglement source, can significantly
compete in the formation of quantum correlations in the thermal state, to the
point that they can destroy any thermal entanglement of the peripheral spins.
