Once read
that it is the detergent which kills bacteria when they eat it in the water, suggesting that cold water is okay. I don't know if that is absolute fact or not. Think of washing your hands. On the other hand, it is always insisted that dust mites in bedding need really hot water to die. I guess it's all up to what kind of micro life you're trying to kill. Then again, sunshine can kill all manner of nasties, even rust stains. Hanging laundry in the sun works wonders.
Once while camping, we washed our clothes in a cold stream, and I was struck by the brightness of the colors as the clothing swirled in the stream.
I use the whole arsenal of temps, sometimes even turning the tank up to HIGH, and sometimes even rinsing in hot water. In winter, however, our cold tap water is very cold, well below 20 C. and it works well on colors, and many here have been using it for years on certain loads. So by default, the answer is yes.
Honestly, for me, water temps are more a function of mood and whim, but if I really want to kill, I use scalding water and Clorox, and, Man, do those mean little bugs scream.