My understanding is not deep.
The simple mental image i keep in my head, and which i use to explain to folks, goes like this:
We know that any metal contains a sea of electrons that are loosely bound, in the very outer shells of its atoms.
That's why metal conducts so well.
We also know that temperature is molecular motion.
Thirdly we know that different atoms have different affinities for electrons.
Pardon the jargon here, trying to paint a simple mental picture:
Heating one end of a wire rattles the atoms there
loosely bound electrons in the hot region are shaken out of their proper place and migrate toward the cool end
causing a small potential difference along the part of the wire that's experiencing the temperature gradient.
Not surprisingly that potential difference depends on the makeup of the wire.
So: if i could measure the voltage between the ends of a single wire experiencing a temperature gradient,
i could plot its microvolts per degree.
Of course that'd be impractical because one of my my voltmeter's wires, the one touching the hot end, would also experience a temperature gradient.
But if i joined two dissimilar metal wires and heated the joint
at their far end i'd measure the
difference between their temperature induced voltages, and at room temperature.I hope this preposterous oversimplification is some help.
We must oversimplify and exaggerate to get our thinking started along a right path
and refine from there.
When our microscopic and macroscopic views come into agreement, and our thought experiments based on the two predict the same results, is i believe when we are beginning to understand.
Imagine those poor guys trying to figure it out before discovery of the electron...
http://thermoelectrics.caltech.edu/thermoelectrics/history.html
old jim