And at the very most, a puppy may go to the bathroom once during the night. Any other barking episodes are not due to this.
What to do: As you go through this advice, keep in mind that these lessons learned now are the foundation for life-long confidence and self-soothing abilities.
When followed, a puppy or dog will learn valuable lessons. If you continue to respond to him when he's barking in the middle of the night, this sort of coddling will not benefit the dog in the long run.
Therefore, the first time that your Maltese barks at night, take him out. Show that this is a very serious time, and not one for playing. Keep lights dim. Do not pat, play with, or speak other than to say 'Good job' for praise if he urinates or eliminates in the designated area.
When done, return him to his area.
For all other barking episodes, ignore and do not approach him. These will be times that the pup learns to look to his belongings to stay busy and self-soothe.
You will find that if he has a 'den' that consists of a bed within a good-sized playpen, a couple of toys that are designed to keep him busy, and a companion toy, that he will learn to turn to those belongings for comfort.
Within 1 to 2 weeks, he will learn that no matter how much he barks you will not appear. And that his energy is best exerted toward elements that offer what he is looking for.