Well in terms of physics, you are trying to create an effect like a convection oven. That's how convection ovens ended up getting started. They were originally just trying to create stable temperature flow throughout and probably didn't realize they'd be going for a while concept of something that would be like we use today.
The idea is to create and circulate the air flow. Igloos use the same idea to keep warm.
So the concept is to have the air flow intake be near the heat source and the exit of the airflow to be at the other side wherever the least heat is, in order to draw that heat towards the weaker side. So you'd point the fan to be going from where the stronger heat side is towards the weaker heat side to balance the two sides out. But this means you'd have to be using your thermometer a lot over time to take readings and sort of figure that part out first; where the stronger heat is and the weaker heat in the box.
To do this, what people also do is have the intake holes lower, and the exit holes higher; because heat rises up.
But for me the hard part is thinking about how to regulate the temperature. Because overtime the heat source going for several hours doesn't stop. And it doesn't have its own thermostat. (At least I'm pretty sure a lot of them might not have a good thermostat, in the sense of how our houses have them.)
You get it? So a simple design has to be done to be affordable. But without a thermostat there's nothing to tell the machine, OK, how do I know when to reduce my own heat?
This is the part I'm worried about now; regulating the heat over time.
It seems like the reading now of the heat won't be the same 2 hours from now, and 6 hours from now with it on all the time. And that's why I get stressed out thinking about it, because I want it to work.
What I'd discovered is that internally a duck's body temperature is actually really high as an average. When you google this it says its 107.5. But the egg nest would be much, much lower. They use the material to regulate the heat. But the eggs themselves would cook wouldn't they if at 107.5 all the time? So there must be more to it than we realize. If the ducks themselves aren't cooking their own eggs and are somehow getting it to work, then humans should be able to figure out how to regulate it also. (If you are doing chickens, well...they must be built slightly differently.) I'm not saying the temperature should be this high. People will say it should be around 99 degrees. Hope I didn't make people freak out. I was just pointing out the natural brood mother's own body temperature is higher than people realize initially before that heat goes in the nest.
Its just maintaining the consistency over time, I guess.
To be fair I'm not an expert and just a beginner, but I was thinking about these questions myself and these are my thoughts, in the hope it will help you to work it out.