You never empty the tank, you refill with some fuel still in it to cool the fuel pump. Think of it as a serial dilution.
To get the full benefit of the cleaner you need to fill the tank, add the cleaner, and run until the tank is low - but obviously not dry.
I don't think overheating of the pump is a problem as long as there's fuel in the tank. A hot pump would cause vaporlock in certain situations, which I don't believe is an issue.