Heidegger's Bible Handbook: Malachi: Chronology

2.  The account of the time in which he prophesied is investigated.

Acquaintance with the time in which he prophesied renders the argument of the Prophecy clearer.  He undoubtedly lived after the construction of the second temple.  For, he does not prophesy concerning matters preceding the construction of the second temple, but only of matters following; and he makes mention of the Temple as now whole, Malachi 1:10; moreover, he corrects many things that are being done sinfully, with the temple now built, such as polygamy, divorce, withholding of tithes, marriage with foreigners:  Nehemiah, in Nehemiah 13, declares that he discovered these things in the time of his government, with the second Temple already built:  finally, he connects his Prophecy with the proclamation of John the Baptist, and recalls Israel to the Law of Moses, to which he commands her to be attached, until the Christ is manifested.  It also appears that he lived in the time immediately after the building of the Temple, when Israel was yet under Governors, of which sort were Nehemiah and Zerubbabel, and so also under the power of the Persians, or of the Greeks, as it is evident out of Malachi 1:8, where he makes mention of the פֶּחָה/governor.