Hot water vs warm water for hot chocolate
There are two good reasons to use boiling water in hot chocoolate.

The first reason is that boiling water helps drive off chlorine which is added to the water supply. This won't work with some chlorine treatment, and of course isn't necessary with bottled or other unchlorinated water, but for standard free-chlorine treatment it can make a big difference. As a rule of thumb, if your boiling water has a distinct (possibly pool-like) smell, it's from the chlorine. (The smell is the chlorine leaving the water. It's still there in unboiled water, but more evident through taste than through smell.)

The second is that cocoa powder may need to be "bloomed" to fully release its flavor. Cocoa powder is a very fine powder, but it's still tiny bits of dried plant matter. Boiling water hydrates these particles much better than hot water, allowing flavor components to disperse into the mixture. The importance of this method varies with the type of cocoa powder you use, and from my anecdotal experience is not as important with European cocoa as it is with North American cocoa.) Failing to do this won't directly lead to bitterness, but the underextracted flavor may make bitterness in the drink more directly evident.

As an experiment, I suggest that you try making "cold chocolate" both ways. Use boiling water as normal, and refrigerate the result to refrigerator temperature. In a separate mug, try making it with cold water. (Add the cold water a bit at a time while stirring, and make sure to scrape the sides thoroughly as you add it; it will not be as easy to mix everything up as it is with hot water. If you end up with a bunch of bubbly, granular mud floating on water, toss it out and try again.) The difference between the two will be evident, and should help you pin down the difference between warm and boiling water.