Back in college we used a big book on 'magnetic circuits and transformers' to work through some of the characteristics of practical inductive components. (I have a copy.) While I don't recommend this for the layman, I want to give a heads up that these things are anything but simple.
First you need to realize that they are not linear. That is, as you increase the voltage applied, the current doesn't follow in proportion. Further, when you raise the input, there is a point at which the core saturates and the incremental inductance drops markedly, causing a rapid increase in current. That's why one needs to respect the ratings. This not only depends on applied voltage but on the frequency of that voltage.
The heat generated comes from two main sources - the core and the windings. Heat is the worst enemy, as it can melt copper and cause smoke to come from insulation, etc.
So if you are seeking a more profound education, realize that there is a lot to assimilate to appreciate these components.