The simple answer is, "a fork mixer will not heat up your dough in the mixing process". A fork mixer has a free spinning bowl and a two pronged agitator that can run at both slow, and fast speed. It is gentle on dough as it mixes, but the mix times are longer when compared to a spiral mixer. But because of the gentle action on the dough, this will help you manage the dough temperature, and achieve your goal temperature. This will result in a higher quality dough that is not heated.
The double arm mixer was one of the first electric mixers. It mixes gently and slowly, which essentially copies the motion of hand mixing. Because the agitation is gentle, the resulting dough is very close in characteristics to that of dough produced by hand mixing. Not much time will be saved in production as it is a slow mix..
The planetary mixer is an all-purpose workhorse found in many bakeries. Planetary mixers are classified as cake mixers, and are not suitable for heavy dough development. Spiral, Fork, and Two arm mixers would be better suited if dough is all you need to make.
The spiral mixer is a single purpose mixer used only for bread and pizza dough development. The smaller spiral mixers, single phase, only have one speed. Most 3 phase spiral mixers have 2 speeds, slow and high speed. Spiral mixers are the preferred mixers of the bread bakers, and pizza makers of Europe. Many bakers see the spiral mixer as the choice that allows speed of production while maintaining control of oxidation and good treatment of the dough.