Is the potency of bleach affected by temperature?

Someone told me once that bleach is “denatured” by very hot water, that for it to be most effective, it should be diluted with cold water. Is there any truth to this?

I always thought the opposite. The hotter the water the more active the bleach will be.

Hence why you usually wash your whites in hot.

Yes, cold water is best. Hot water drives out the free chlorine as a gas and it leaves the solution into the air. Cold water lets the free chlorine stay dissolved.

That’s right, raising the temperature increases the rate at which the sodium hypochlorite(bleach) reacts with proteins, as well as the rate at which it converts into powerfully oxidizing chlorate ions. Chlorine gas is not a normal part of the bleaching process; instead the bleaching is done by hypochlorite and perchlorate ions.
For more than you want to know, see How does chlorine bleach work and the associated links.

I suppose it all depends on what you want the bleach to do. If you want to remove colors etc, then boiling is probably good because it rapidly releases the effective agents. If you want to use it as a disinfecting solution, then cold water is best because it retains its disinfecting qualities longer.