The Christmas Song was written during a blisteringly hot summer in 1945 by Mel Torme and Robert Wells with the thought that they had of “think cool to keep cool”. Torme had seen some notes on Well’s piano they read: chestnuts roasting, Jack Frost nipping, Yuletide carols, dressed up like Eskimos. Within a few minutes, he had written the tune and most of the lyrics quickly followed.
It was first recorded by the Nat King Cole trio in 1946 and quickly became a huge hit. Here is a link to Nat King Cole’s version.