OED has "let off steam" from 1831, and the phrase refers to a steam

engine. This is from April 1831, pg. 363:

It was not well advised, then, in a friend of John Richards, instead of

removing doubts, known to exist, as to the purity of that family, to have let

"off the steam" in criminations of the gentleman who instituted the inquiry,

through the columns of your Magazine....