I hope you will report back to us if, through your experimentation, you can establish a more causal connection between hand kneading and a materially elevated finished dough temperature,
The causal connection is that hand kneading introduces an additional source of heat that is not present in mechanical mixing. With mechanical mixing, the only significant additive source of heat is friction, both between the dough and the mixer and within the dough itself. In addition to these heat sources, hand kneading involves the radiative and conductive heat transfer from one's hands to the dough. So with a mechanical mixer, the dough hook starts out somewhere near room temperature, but with hand kneading, the "dough hooks" start out in the neighborhood of 93-94° F—normal core body temp is 98.6° F, but the skin rarely reaches core body temp.—and blood circulation ensures that something close to that temperature will be maintained throughout the kneading process. Combine that with the fact that:
a) humans are homiothermic (warm blooded);
b) the excess energy generated by muscular activity is expelled primarily through the skin as waste heat;
c) excess body heat is transferred more efficiently via
conductive transfer than radiative transfer; and
d) at rest, the human body puts out approx. 18.4 btu/hr ft^2, i.e.
every square foot of body surface (skin) puts out approx. 18.4 BTU/hr* (during strenuous exercise, the heat output can be as much as 40x that);
and it should come as no surprise that hand kneading introduces a significant amount of heat into the equation that is not be present in mechanical mixing.
Of course, calculating the requisite starting temp for the water would be damnably difficult, because one would need to know, inter alia,
the amount of heat generated by hand kneading, which would depend on the level of activity (light, medium, strenuous), the surface area of contact, the mass of the dough (obviously, more heat is required to raise the temperature of a 2 lb ball of dough 1° than a 1 lb. ball), and the length of contact between between the hands and dough (kneading time), but if anyone feels the need to do so, be my guest!
* The skin surface area (Du Bois area) of an average adult body is approx. 19.36 ft^2, meaning that the average adult at rest
sheds approx. 356 BTUs/hr—roughly the amount of heat put out by a 100-watt lightbulb—in the form of waste heat. The Du Bois area normally varies between 14 ft^2 and 23.7 ft^2, so in any setting the heat produced by sedentary adults will vary between 257 BTUs (75.6 watts) and 436 BTUs (128 watts).