Origins
The word 'warm' is one of the great showcase examples of Indo-European comparative linguistics, because its cognates across multiple language branches illustrate the regular sound correspondences that allow linguists to reconstruct PIE with confidence. It descends from Old English 'wearm' (warm), from Proto-Germanic *warmaz (warm), from PIE *gʷʰer- (hot, warm).
The PIE root *gʷʰer- underwent different sound changes in different branches according to the regular laws that define each branch. In Germanic, the PIE labiovelar aspirate *gʷʰ became *w (part of Grimm's Law, the systematic Germanic consonant shift), giving Proto-Germanic *warmaz and eventually English 'warm,' German 'warm,' Dutch 'warm,' and Swedish 'varm.' In Greek, *gʷʰ became 'th' (θ), giving 'thermós' (θερμός, hot) — the source of 'thermal,' 'thermometer,' 'thermos,' and 'hypothermia.' In Latin, *gʷʰ became 'f,' giving 'formus' (warm) and 'fornāx' (oven, furnace) — the source of English 'furnace.' In Sanskrit, *gʷʰ became 'gh,' giving 'gharma' (heat). In Armenian, it gave 'jerm' (warm).
These correspondences — English w : Greek th : Latin f : Sanskrit gh — from a single PIE sound are one of the foundational discoveries of historical linguistics, first described systematically in the nineteenth century. The word 'warm' is routinely used in introductory linguistics courses to demonstrate how a single proto-form can yield radically different-looking words in daughter languages through regular, predictable sound change.
Figurative Development
The figurative uses of 'warm' are deeply embedded in English and reveal systematic metaphorical thinking. 'Warm' means emotionally kind and welcoming ('a warm person,' 'a warm welcome'), because physical warmth and emotional closeness are mapped onto each other in English conceptual metaphors. 'Warmth' refers to both temperature and personality. 'Warm-hearted' means kind and generous. 'To warm to someone' means to begin to like them. The opposite pattern holds: 'cold' means emotionally distant. This temperature-emotion metaphor is not universal — some languages map social closeness to other physical sensations — but it is deeply entrenched in English.
The verb 'to warm' (to make warm, to heat) dates from Old English. 'To warm up' (to prepare for activity) dates from the nineteenth century, originally in sporting contexts — loosening muscles by generating heat through preliminary exercise. 'Warming' as in 'global warming' dates from the 1950s, though the scientific concept was described by Svante Arrhenius in 1896.
The 'Thermos' brand (a vacuum flask for keeping liquids warm) was trademarked in 1904, taking its name directly from Greek 'thermós' (hot). It has since become a genericized trademark in many countries — a common noun derived from a proper noun derived from an ancient adjective that shares its root with the English word 'warm.'