In a warm manner, showing affection, enthusiasm, or kindness.
From Old English 'wearm' meaning hot or heated, plus the adverbial suffix '-ly'. The figurative sense of emotional warmth developed in Middle English, extending the physical concept of temperature to describe human feelings and social interactions.
The metaphorical leap from physical temperature to emotional tone is found in many languages, reflecting a universal human tendency to describe abstract feelings through concrete sensory experiences. Interestingly, research shows that holding a warm cup of coffee actually makes people judge others as having 'warmer' personalities!
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