Temper; (Webster)
[<AS & OFr <L Temperare]
1 - To make suitable, desirable etc by mingling with something else; moderate, as mingling criticism with reason
2 - To bring to the proper consistency, hardness etc by treating in some way; as to temper steel by heating & sudden cooling.
Thus the roots of this word "Temper" are far older than either us Americans or you Brits. The word itself describes the "Process" thus you "Temper the Steel", you do not "Give it a Temper", so there is No Temper to draw.
In most cases a piece of heat treated steel is thus tempered twice. The first temper puts it in its stage of maximum hardness, while the 2nd temper reduces the hardness to the level desired.
Now in America we do not normally refer to the hardening process as tempering only hardening. The second process we then call tempering. Is this 100% correct, I don't know for sure, but I do know it is far more correct than saying you "Draw the Temper" regardless of how long you Brits have used the terminology.
IE, You Brits did not "Invent" the word, only misused it.