1520s, of feelings; 1590s, of temperature, from warm (adj.) + -ly (2).
Entries linking to warmly
warm adj.
Old English wearm "warm," from Proto-Germanic *warmaz (source also of Old Saxon, Old Frisian, Middle Dutch, Old High German, German warm, Old Norse varmr, Gothic warmjan "to warm"), of uncertain origin. On one guess it is from PIE root *gwher- (source of Greek thermos "warm;" Latin formus "warm," Old English bærnan "to kindle"). On another guess it is connected to the source of Old Church Slavonic goriti "to burn," varŭ "heat," variti "to cook, boil;" and Lithuanian vérdu, virti "to seethe."
The use of distinct words, based on degree of heat, for warm and hot is general in Balto-Slavic and Germanic, but in other languages one word often covers both (Greek thermos; Latin calidus, French chaud, Spanish caliente). In reference to feelings, etc., attested from late 15c. Of colors from 1764. Sense in guessing games first recorded 1860, from earlier hunting use in reference to scent or trail (1713). Warm-blooded in reference to mammals is recorded from 1793. Warm-hearted first recorded c. 1500.
-ly 2
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.