Broody hens consistently hatch and raise chicks in those temperatures. The temperatures may be a contributing factor, but I suspect it's how you are handling the eggs in that heat that's the problem. Getting zero just doesn't sound right.
When and how are you collecting them? Where are you storing them and what are the conditions? How long are they stored before incubation starts? Have you checked for the bull's eye to see that they are fertile?
There are several things that can reduce the chances of an egg hatching. Most of those don't make sense or you but I'll go over some. You may see something since you are there looking at them.
I know with three roosters it doesn't make sense but have you checked for the bull's eye to confirm that they are fertile? Eliminate the obvious. Also, did you open the unhatched eggs from those two unsuccessful tries to see if any started to develop and when they stopped? That might be your biggest clue. It's what the professionals do, open unhatched eggs.
If the eggs are badly shaken they don't hatch very well. Storing them up-side-down or not turning them before you give them to the broody can reduce hatchability but not to that extent. Actually a very small extent so that is not it. I'll just mention them to get it out of the way. But shaking can be serious.
The longer they are stored, especially in poor conditions, the less likely they are to hatch. I can't imagine you keeping them long enough for that to be a big problem, not at a zero hatch level.
What temperature did you store them at? Did you refrigerate them? Different refrigerators are set at different temperatures. Often you can get some refrigerated eggs to hatch, sometimes they hatch well, but if your fridge is set really cold it may be enough to stop them from hatching.
How warm was where you stored the eggs? Did you cook them, either in the nests or where you stored them, before incubation started? Are the broody nests somehow where they could be cooking in the nets during incubation. Maybe in the sun? I've seen broody hens stand in the nest over the eggs to allow them to cool off. If it's not hot enough there to kill your broody hen that nest is probably not hot enough to cook the eggs. But, as with all this, you are looking at them.
There are diseases that can prevent the eggs from hatching but if your flock is acting healthy it is unlikely that a disease is your problem.
Opening the unhatched eggs is probably the best way to determine where to at least start looking.
I wish you luck with this, it can be really frustrating.