Depends upon which oxygen bleach.
Perborate bleaches will start working at around 120F or so, but really need 140F and higher water temps to really get going. OTOH, percarbonate bleaches work in all water temps, but really get going at 100F. Mind you all oxygen bleaches work slower at the cooler end of their ranges, so contact time must be increased as temps go below 100F or so.
Perborate bleaches were inexpensive and when most wash (at least in Europe) was boiled or done at very high temps, it worked well. Persil was the first detergent to combine perborate bleach (PERborate -SILicate ='s PERSIL). However as laundry temps began to drop from boiling to 120F-140F or lower, bleaching activators were added to give the same results with cooler water. Also because of bleaching activators such bleaches would work with shorter contact time, despite cooler water. This is one of the reasons Persil and other activated oxygen bleachs/detergents came out with a colour version. Repeated laundering of dark and or some coloured items with normal Persil eventually lead to bleaching/fading of colours.
Percarbonate bleaches OTOH as stated do work in warm and in some cases cold water, but again contact time must be increased as water temp drops, unless activators are used.
As for wash temps and "over kill" it depends upon what one is laundering. If trying to restore whiteness/remove stains from sturdy white/colourfast items, then hot or boiling water temps with oxygen bleach will do the trick quite quickly. One must remember to as temps go higher to limit contact time, say at 180F to 200F, no longer than 10-15 minutes. On the other hand if trying to remove stains from delicate items or anything that would be harmed by very hot water, longer contact time with cooler water (100F to 120F) is best.
Just as an aside, oxgyen bleaches are called "colour safe" because of several reasons. First, neither perborate or percarbonate bleaches can remove colourfast dyes. Though darks and some other colours can fade with repeated use, especially in with hot water. In the case of perborate bleaches, because it needs hot or very hot water to really get going, the warm water temp normally used for laundering colours is not going to activate perborate's bleaching activity to the extent to cause damage. All oxygen bleaches work by attacking organic colour matter such as tannins. Man made chemical dyes normally are stable, but always test before hand.
L.