I’ve heard you say that the temperature of the dough after mixing is the single most important aspect of dough management. Would you please explain this to me?

The temperature of the dough is vitally important because it sets the stage for everything else that will happen to the dough thereafter. It is the temperature of the dough that controls fermentation, how fast it will proceed, and how long it will continue for. For example, higher dough temperatures allow for faster fermentation rates, as the dough ferments faster, it consumes more nutrient (sugar) and generates more acid (acetic. lactic and propionic). The ultimate lack of nutrient and excess of acid work to significantly slow or halt yeast activity after several hours in a typical pizza dough formula. Cooler dough temperatures will slow the rate of fermentation, decreasing acid formation and nutrient metabolism, allowing for a longer sustained fermentation period for the dough. Also, from a mechanical point, doughs having a lower temperature are easier and faster to cool when taken to the cooler. Doughs that are too warm, may be difficult to cool efficiently resulting in over fermented, or “blown” doughs. So, as you can see, if the dough temperature is not controlled, your entire dough management procedure can become unraveled overnight, resulting in lost doughs, or at best, inconsistent dough performance or finished product quality characteristics.

How important is it to have the water temperature right at the recommended 100 F to 105 F for activating my active dry yeast?

The water temperature used to activate any type of dry yeast is really pretty important if you have a concern over yeast performance, and I think we all have an interest in that. In al cases, active dry yeast must be hydrated before it can be added to the dough, and in some cases, instant dry yeast must also be hydrated. Take note that the correct water temperature to use when hydrating IDY is 95 F. If the water temperature is too hot the yeast cells can be heat/thermal damaged, but if the water is too cold, you stand the risk of allowing some of the plasma material contained within the yeast cell(s) to leach out during the hydration process. This material, when removed from the cell, can result in the development of an unusually soft or in some cases sticky dough consistency, and extensive damage to the yeast cells from which the material was removed. All in all, good things do not happen when dry yeast is allowed to hydrate in water at a temperature other than that which is recommended by the manufacturer.
Also, while we’re on the topic of hydrating dry yeast, keep in mind that when the directions say to hydrate the yeast in water at say, 100 to 105 F, only a small quantity of the total water needs to be at that temperature, only about five times the weight of the yeast. The rest of the water should be at a temperature that will give you a finished dough within the desired or targeted, temperature range.