When washing dishes what works better warm or cold water?

Your boyfriend is right about germs, but that isn't the reason you want to use warm water. The solubility of substances in water increases as the temperature goes up. Using warmer temperatures greatly increases the water's ability to remove polar stains on your hands, and aids in the formation of micelles (of the soap molecules). This helps the soap molecules to dissolve the non polar oils and greases faster.

As for warm water being a breading ground, drying your hands right away and using running water should help with that.