For the most part, you are on the money but also posted a few things that are either completely inaccurate or could easily be interpreted the wrong way. I highlighted some key points in bold.
First off, I will address the later points:
1. It (a chicken) creates it's OWN warmth... using calories. A calorie is a calorie is a calorie:
    - It's a fact that food, itself, does not create heat. The chicken's (or animal's) body creates heat through the metabolic process using calories so a calorie/kcal is the same value regardless of where you get it from. I kcal from corn is the same as a kcal from pellets or wheat or peas. But that also means more calories from any source still means more calories and this is where corn comes in.
2. Corn does NOT make them fat:
    - Feeding all corn vs a 16 or 18% protein pellet/crumble diet and you will see the difference. Not only is corn easier for chickens to digest, meaning it gets converted into usable energy fastest for chickens compared to other grains, it also has the highest available energy per lb, which we use calories/kcal as the unit of measurement of for energy.
Corn has 1510-1530 kcal/lb.
16% protein pellet/crumble/mash contains 1210-1240 kcal/lb.
20% protein pellet/crumble/mash contains just 1290-1320 kcal/lb.
As you have noted, a simple bio course here and there and you should know about how the body works and what happens to unused calories; they turn into fat which in turn is used to heat up the body and/or keep the body warm. You even mentioned eating a bunch of high calorie food such as junk food items like candy bars will make you fat. There's a reason for it; it's because it's small yet contains a high amount of calories.
3. NORMALLY they stop when they are full... and have met their caloric need for the day.
    - Unlike humans, animals do not know when they have met their caloric need. They don't have a caloric chart or recommended caloric intake advised to them by other chicken scientists and they certainly don't understand what we tell them 

. Heck, as humans, without a chart or being told, our body does not tell us to stop when we have met our caloric need for the day. We, much like chicks and any other animal, simply eat until we have had their fill. It doesn't matter if it is pellets or corn so if a chicken consumed. Using the widely accepted 1/4 lb of feed a day, 
in a month a hen will have consumed about 7.5lbs of feed. This is where the difference in calories comes into play.
7.5lbs of corn = 11,400 kcalories
7.5lbs of 16% = 9,188 kcalories
So over the course of a month, a hen fed only on corn consumes over 2,200 more Calories than a hen on 16% feed and that's key to this whole "don't feed too much corn or your chickens will get fat" conversation. The chicken does not know it has eaten taken in more calories, it does not know it needs to "run", "scratch", and "fly" more to lose the excess calories. And we all knows what happens to unused calories and that's why feeding alot of corn, or even solely corn, will end up making a chicken fatter, which will help them retain their body temperature better which ends up keeping them warmer.
Outside of a few keypoints, very good post