If you don't want to use hot water, Stop Foodborne Illness recommends using a sanitizing solution. One tablespoon of unscented chlorine bleach per gallon of water is enough to effectively sanitize your dishes. Your dish rags are really no better than your sponges. And like sponges, using a dirty dish rag to clean a kitchen countertop will only spread germs. Your best bet is to replace rags about once a week.
After washing your dishes with soap and Hard Water Dishwasher Detergent to remove any left-over gunk, Warriner and Narvaez both suggest soaking them in warm water and one teaspoon of bleach to sanitize. If you're wary about using bleach, soak dishes in hot water (at least 77 degrees Celsius) for two minutes to kill any remaining bacteria.