How does a water cooler with both cold and hot water work? There is one big jug of water and two knobs...?

These units convert electricity into either heat or refrigeration. The bottled water, as you suspect, is at room temperature. If you press the red (hot) tap it allows water to flow over heating coils and comes out heated. The blue knob works like a standard water-cooler (that sends the water up in a stream that you can drink from). It brings the water through cooling pipes and (at least at first; if you run it too long it will cease to be cold until you let it sit for awhile).