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Temperature is important

There is an optimal temperature for a dough that just finished mixing and kneading. This has to do with the premise that you are now going to bulk ferment the dough and depending on the dough's contents, fermentation gets the best results (from a flavor perspective, which depends on speed, flour and mixing) when it starts at a certain temperature. If your source specifies this temperature (example is the CIA's Baking and Pastry book), you use it. Otherwise 78F, or 79F is a good guess.

The temperature of a mixed dough depends on the temperature of the main ingredients, being the flour, water (or milk etc.), and any preferments.

Contributions to final dough temperature

The following portion of the "Recipe" worksheet will aid in explaining what is going on:

Water Temp Table

In this example, the main temperature contributors to the final dough are (a probe thermometer is your friend for all this):

Thus, in the example (which assumes 47F water source), we see that we need to warm up the water a bit, and no ice is needed. You will find that the "Water Corrected" is identical to what the basic formula lists.

TIP: As an alternative, and if you do not want to bother with precise ice measurements and crushing ice, just add some ice cubes to the water to cool it below the desired temperature. Use the microwave to correct it back up to what you need. This obviously only works if the water temperature you are looking for is above the freezing point.

How the calculation is done

The calculation is not correct from a physics perspective, but is a reasonable approximation, again under the assumptions that the ingredients listed have a roughly equal contribution. The basic formula (for degrees Fahrenheit) is to multiply the desired dough temperature by the number of temperature contributors involved (4 in this example: room, flour, preferment, mixer) and subtract each contributor's temperature.

This approximation has been used for a long time, and succesfully at that, so why is this? Remember that you have to emperically determined your mixer friction factor for each specific dough and setup? Differences from the above calculation are caused by:

The differences from the above calculation are all absorbed into the friction factor that you come up with. Thus its name is a little misleading in that it not only accounts for mixer friction (which is often the majority of it), but also for all these other changes.

Note that while for all contributors except mixer friction, we input an actual temperature, and conversions from Fahrenheit to Celcius are provided (and show the expected values). Mixer friction, however, is a temperature difference and hence conversion to the equivalent amount in Celcius is not the same. A normal conversion from F to C involves subtracting 32 (freezing temperature) and multiplying by 5, dividing by 9. For a temperature difference conversion, you leave out the subtraction of 32 (because it cancels out). Thus a mixer friction factor of 40F is equivalent to 22.2C, and not to 4.4C!

If the calculated water temperature would come out to be below freezing, we have a problem. We can't get ice out of the tap, let alone ice of a specific temperature. Converting ice into liquid water takes substantial energy. If we add ice to the dough mix and it converts back to water, it needs this energy, which is extracted from the rest of the ingredients, cooling the dough.

The amount of ice needed (in pounds) is computed by multiplying the total weight of all liquid ingredients, expressed in pounds, by the difference in temperature between the source water and the desired water temperature and then divide by the sum of source water temperature and 112. This is the formula for Fahrenheit. If you are working in Celcius, express the weight in kilograms, and instead of 112 use 80 (the original 112 + 32 from the conversion from F to C, multiplied by 5/9). This will give the amount of ice in kilograms.

The ice should be flaked or crushed ice in order to increase the contact surface and to facilitate the liberation of the latent heat.

Here is a copy of an article from Baker's Exchange that goes into more detail and examples.