Today, the French words "trempe de l'acier" correspond to quench hardening of steel. However, during centuries, this operation was called "tempering", and quenching was only "immersing into water", without implication of a result. The verb "to temper" (as tremper) is coming from the Latin "temperare", which means "to moderate". The histories of "tempering" and "trempe" are quite similar. The term tempering was frequently employed to include the entire process of preparing a piece of steel, including heating, hardening, and "partial annealing", until the end of the 19th century. This softening is now called: tempering, that is finding a compromise between hardness and brittleness, which corresponds to the signification of "temperare". This first paper exposes, the different treatments called "trempe/tempering", then the control of temperatures, the quenching baths sometimes of magic compositions and the defects produced. The last paragraph relates the history of the technical words since Homer, through the Middle Age, and until the normalisation at the end of the 19th century. A second paper will describe the slow evolution of the explanations of steel hardening by quenching in water. They were based on the conceptions of the structure of matter inherited from Aristotle, until new crystallographic and atomic concepts appear in the first years of the 20th century, which are exposed in a third paper.