This is an extremely rare word, meaning the process or action of becoming warm or hot. In 1888, the New York Sun (surely the most appropriately named journal to lay claim to it) included it in a squib that borrowed the shade of Dr Samuel Johnson to complain magniloquently about the perils of riding a commuter train in the city on cold winter days:
“Sir,” said Dr. Johnson, “the corporeal gelidity and horripilation superinduced by the niveous atmosphere cannot be mitigated even by the mental incalescence evolved by indignation.” “He means,” whispered Mr. Boswell, “that it’s so infernally cold in the cars of the Third Avenue elevated that even swearing at the directors won’t warm you.”
Incalescence dates from the early seventeenth century; it was one of many words that were imported from Latin by scholarly writers around this time, in this case from incalescere, to become warm or hot. That’s from calere, to be warm, which is also the source of calorie, calorimeter, and other words.
Another rare appearance was in The Ladies’ Repository of December 1866: “What the flexible imagination is to the ordinary activity of the mind, the fiery is to its creative energy. Little depends upon the degree of its incalescence — more upon its living, energetic, thoughtful activity and rapid but thorough progress.”
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