Are there "eccentric seasons", where do they occur, and why don't we hear more about them? The earth is on an eccentric orbit. It's a small eccentricity (let's say e=0.01 https://www.wikiwand.com/en/Orbital_eccentricity) but it's there.
As it moves closer and farther from the sun the amount of energy being absorbed from the sun's light will change, and thus there will be a temperature shift dependant on earth's eccentricity (an "eccentric season")
The flux on earth and thus the rate it which it absorbs the sun's energy goes as r^-2, where r is the orbital radius. Thus the fractional change in flux is proportional to 4e. (taking into account the factor of 2 from the orbit ranging from a(1-e) to a(1+e) where a is the semi-major axis)
The effective temperature (assuming a blackbody) goes as (P)^0.25, where P is the incident power (= flux on earth * cross sectional area of earth).
Thus, for small e the fractional change in temperature should be ~ e.
For Earth, with a temperature of roughly 300 K, this gives a 3 degree temperature shift over an orbit.
I'm not sure I've ever heard anyone talk about this, and it doesn't seem negligible (especially given that there are parts of the world where seasonal temperature changes only by about 10 degrees http://ggweather.com/sf/narrative.html).
So my three questions are:
a) Is the above logic correct, are there (small) "eccentric seasons"
b) Where would they occur, specifically what latitude if any has a boosted seasonal change?
c) Is this something talked about that has just passed me by (wouldn't be the first time)?
 A: Eccentricity plays but a minor role in the seasons. Eccentricity would lead one to think that the Earth as a whole should be warmest in early January when the Earth is near perihelion, coolest in early July when the Earth is near aphelion. The reality is that exactly the opposite occurs, at least currently. The Earth as a whole is at its coolest in January and its warmest in July.
The key driver in the seasons is the Earth's axial tilt. This is why the seasons run counter to one another in the northern and southern hemispheres. Next in line is the very different distribution of land in the northern and southern hemispheres. That the southern hemisphere is predominantly water moderates its seasons. That the northern hemisphere has much more land mass makes its seasons more extreme.
Eccentricity does play a role in the seasons in the long term. Glaciations ("ice ages" colloquially, but that term is incorrect; the Earth remains in an ice age to this day) generally start when northern hemisphere summers are mild and end when northern hemisphere summers are hot. The long but mild northern hemisphere summers that result when summer in the northern hemisphere coincides with aphelion don't get warm enough to melt winter snow in far north latitudes. Those mild summers means winter snow at 65° N latitude can remain on the ground all summer long. The snow builds up over the centuries to form sheets of ice that are multiple kilometers thick . On the flip side, those multiple kilometer thick accumulations of snow and ice melt in the face of the short but fierce summers that occur when northern hemisphere summer coincides with perihelion.
