Another derivative of צהר is צוהר which can be a window, hatch, porthole on a ship... Basically, it is an opening in a structure designed to let in light.
The ancient Book of Job mentions the bits of light that pierce through the ceiling of a tent (nomadic, thick, black goat hair permanent structure) during the day as being like the bits of light piercing through the night sky (which are actually stars). The point is, this word צהריים quite possibly comes from the hatch in the sky that allows a lot of light through (which is actually the sun). Mid-day/noon, of course, is the time of day that there is the most light. However, this word looks, to me, to be signifying 2 hatches, which I'll have to ponder more unless someone else wants to chime in here.