Warm water speeds up the action of the yeasties, and is not necessary for the yeasties to start working. I have used the Reinhart recipe many times with great results and have always followed it and used room temp. water. I suspect that when making the sponge in this recipe, you don't want the yeasties to work too fast. The timing of the sponge's rise and its mixture into the other ingredients is kind of critical. You want to mix it with the other stuff just before it collapses.
Too fast yeastie action will result in too much alcohol being created and a chemically taste in your bread. Or the sponge will run out of live yeasties and fail to rise the rest of the dough properly. Or both.
The windowpane test is a way of determining if sufficient gluten has developed in the dough. Gluten is a protein that develops when flour and water are mixed together. Kneeding speeds up the process of gluten development.
How to do a windowpane test (from Sourdough Home - Basic Yeasted White Bread
Once the dough is springy and lively, it's time for what bakers call "the windowpane test". Start by pulling off a piece of dough about the size of a walnut. Roll it between your hands for a few seconds to smooth the damage done when you pulled the dough away from the larger chunk of dough. Now, using both hands, pull the dough between your hands. The idea is to tease the dough into a sheet or film. From time to time, rotate the dough 90 degrees so you will be pulling on different sides. As you pull on the dough, it should form a sheet, or film, that is thin enough that light can pass through it. No, you won't be able to see things through it, like you could with a real window. The dough shouldn't tear when you do this.
If you can form a windowpane, the dough is fully developed. If you can't, then knead another 5 minutes or so. When I made this bread, I formed a windowpane after about 10 minutes of kneading. I should have kneaded it a bit more. This will not work with breads that have lots of stuff - like nuts, seeds, raisins and so on - in them. But after you do this a few times, you'll know how your dough should feel.