There have been two attempts to explain the variations in the natural
noon cycle with the most recent attempt in the late 17th century being
the most improbable.The introduction of celestial sphere geometry into
heliocentric reasoning and especially the motions of the Earth created
a hoax that is known as the 'analemma' -

http://en.wikipedia.org/wiki/Analemma

Attributing a variable inclination to the Sun as a component of the
global variations in length of the natural noon cycle does not warrant
comment.

The next attempt is by Kepler who applied a global solution,while the
premise and conclusion is false,it is far superior to the 'analemma'
view given that Kepler assigned a variable daily rotation to the Earth
-

'How does the Sun strengthen the motor virtue of the Earth by
increasing the diurnal revolutions of the Earth'
"It is very probable that this takes place by mediation of the light
of the Sun which the Sun pours upon the Earth,through the illumination
of the Earth's hemisphere.For because the additosubtractive [aequatio]
of time demands daily unequal revolutions of the Earth,according at
its distance from the Sun varies..." Kepler

The actual cause of the observed natural noon variations remain two
separate 360 degree motions with respect to the Sun.The first is
daily rotation through 360 degrees in tandem with the slow 360 degree
orbital change with respect to the central Sun over the course of a
year,that slow turning occurring in accordance with Kepler's view of
variable orbital speed and geometry.