Food Scientists: Please Explain the Final Dough Temperature (FDT) Formula
If kneading does not significantly heat up the dough, and the process is sufficiently quick then, by basic thermodynamics, the final dough temperature (FDT) is the average of the temperatures of the ingredients. (JoutlawPhysics points out in a comment below that this assumes equal masses of ingredients, which is usually only approximately true.) Hence

FDT = (water temp + room temp + flour temp + preferment temp)/4.

Here 4 is the `multiplication factor'. In general the multiplication factor is the number of temperatures involved, minus one. Rearranging the formula above we get

water temp = FDT*(mult. factor) - room temp - flour temp - preferment temp.

Your formula is the small generalization allowing for the heating effect of friction during kneading or mixing of the dough.