Old English hat "hot, flaming, opposite of cold," also "fervent, fierce, intense, excited," from Proto-Germanic *haita- (cf. Old Saxon and Old Frisian het, Old Norse heitr, Middle Dutch and Dutch heet, German heiß "hot," Gothic heito "heat of a fever"), from PIE root *kai- "heat" (cf. Lithuanian kaistu "to grow hot").
The association of hot with sexuality dates back to c.1500. Taste sense of "pungent, acrid, biting" is from 1540s. Sense of "exciting, remarkable, very good" is 1895; that of "stolen" is first recorded 1925 (originally with overtones of "easily identified and difficult to dispose of"); that of "radioactive" is from 1942.
Hot flashes in the menopausal sense attested from 1887. Hot air "unsubstantiated statements, boastful talk" is from 1900. Hot stuff for anything good or excellent is by 1889. Hot potato in figurative sense is from 1846. The hot and cold in hide-and-seek or guessing games are from hunting (1640s), with notion of tracking a scent.