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We report the existence of entangled steady-states in bipartite quantum magnonic systems at elevated temperatures. We consider dissipative dynamics of two magnon modes in a bipartite antiferromagnet, subjected to interaction with a phonon mode and an external rotating magnetic field. To quantify the bipartite magnon–magnon entanglement, we use entanglement negativity and compute its dependence on temperature and magnetic field. We provide evidence that the coupling between magnon and phonon modes is necessary for the entanglement, and that, for any given phonon frequency and magnon–phonon coupling rate, there are always ranges of the magnetic field amplitudes and frequencies for which magnon–magnon entanglement persists at room temperature.