The main reason why you use warm water instead of cold is because together with the detergent (if you use any) the warmth will help to dissolve the greases that keep food stuck to your plates and utensils. That way you flush the bacteria out. Maybe the soap will kill them but then likely they'll be down the drain anyway.

The only stuff that warm water doesn't work well for are as far as I know dairy products and egg-white, because they solidify when warmed up.

Also, there is not much point in thinking you're killing bacteria and then using a dirty dishrag to dry off the dishes :)

Bacteria are pretty hardy, some of them even survive at temperatures above 300 degrees celsius, but you're not likely to run in to them in the home (unless you live in a sulphuric hot spring).

edit: I hope that's 90 degrees Fahrenheit you are referring to.