Old English steam "vapor, fume, water in a gaseous state," from Proto-Germanic *staumaz (source also of Dutch stoom "steam"), of unknown origin. Meaning "vapor of boiling water used to drive an engine" is from 1690s, hence steam age (1828) and many figurative uses, such as let off steam (1831, literal), blow off steam (1857, figurative), full-steam (1878), get up steam (1887, figurative). Steam heat is from 1820s in thermodynamics; as a method of temperature control from 1904.
We have given her six months to consider the matter, and in this steam age of the world, no woman ought to require a longer time to make up her mind. [Sarah Josepha Hale, "Sketches of American Character," 1828]
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy). Adjectives such as hugy, vasty are artificial words that exist for the sake of poetical metrics.
<a href="https://www.etymonline.com/word/steamy">Etymology of steamy by etymonline</a>
Harper, D. (n.d.). Etymology of steamy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/steamy