Heidegger's Bible Handbook: Deuteronomy: The Chronology of Deuteronomy
The book narrates the history of roughly two months. For the address made in the name of God to the people, which is narrated at the beginning of the book, happened on the first day of the eleventh month of the fortieth year from the Exodus, Deuteronomy 1:3. But Moses died, according to Josephus at the end of book 4 of his Antiquities, in the last month of the year; namely, on the first day of that month, which is called Dystrus by the Macedonians, Adar by the Hebrews. Now, the Israelites mourned their dead Leader on the plains of the Moabites for thirty days, Deuteronomy 34:8, and so for the whole twelfth month. And so in the space of the two last months of the fortieth year after the Exodus, of the end of the exile in the wilderness, the matters narrated in Deuteronomy are concluded.
 This correlates with February-March (late winter) of the present calendar.