His paternal grand-uncle was Dominic Burke, O.P., who opposed the Papal Nuncio, Giovanni Battista Rinuccini.
His maternal grand-uncle was John de Burgo, Archbishop of Tuam, and Hugh Burke, Bishop of Kilmacduagh (1647 – ca.
O'Heyne received the habit at Athenry on 4 August 1664 and left for Spain in 1667.
Upon his return to Ireland he became preacher and master of novices at Drogheda, where he became acquainted with Oliver Plunkett.
James Hardiman called him "a learned and ingenious historian" on account of his works on Irish Dominican history.