Science will tell you that yeast prefers a narrow range of temperatures, and that it grows much faster at those temperatures. Experience tells me that unless the water is hot enough to kill the yeast, you have a much wider range of temperatures that are perfectly safe for the yeast.
It’s interesting that although the general consensus is that a long, slow cold rise is best for flavor development in yeasted doughs, most recipes start off with relatively warm water.
There’s a reason for it. If you’re proofing yeast, you want that step to happen relatively quickly, so it makes sense to use water that’s the optimum temperature for the yeast.
But what is the optimum temperature? And is it the same for all yeast?
For active dry yeast, the water temperature should be between 105 and 110 degrees for proofing. While 95 degrees is the best temperature for yeast to multiply, that’s not quite warm enough for proofing active dry yeast. It needs the extra warmth to dissolve and become active. At cooler temperatures, the yeast doesn’t wake up as well, and it can release a substance that can interfere with gluten formation.
For fresh (cake) yeast, 95-100 degrees is what you’re looking for during proofing. Cake yeast doesn’t need to dissolve, it just needs to start feeding and multiplying.
For rapid rise or instant yeast that will be mixed with the flour rather than added directly with the water, the suggested water temperature is significantly warmer. Package directions suggest that water of 120-130 degrees should be added to the flour and yeast mixture. I suspect higher water temperature compensates for the room temperature flour. While instant yeast doesn’t require proofing, if you’re not sure of the viability of the yeast you can proof it the same way you’d proof active dry yeast, at 105-110 degrees.
When instant or rapid rise yeast is used in a food processor recipe, it’s common for cool water to be added to the flour while the processor is running. This makes sense because the action of the processor heats the dough significantly. If warm water was added, the dough could heat up to a point where it could kill the yeast.
If active dry yeast is used in a food processor recipe, it’s common to proof the yeast in a small amount of warm (105-110 degree) water, then add a larger portion of cool (or even cold) water to the food processor after the yeast mixture has been added.
While there’s some downside to using water that’s a little too cool for the yeast, water that’s too warm - between 130 and 140 degrees - is fatal to yeast. So, if you can’t measure the temperature accurately, it’s better to err on the side of coolness.
An instant read thermometer is an accurate way of checking water temperature, but you can certainly make a yeasted dough without one. People were successfully using yeast long before instant-read thermometers were common, and moms have been checking baby bottles the same way for a long time. Water at just above the 100-degree mark will stop feeling cool to the touch and will feel comfortably warm - not at all hot. At that temperature, your yeast should be perfectly happy. It might not be optimum, but it will work.