evening runner, you can't take the Sun angle out of the equation, the Sun's effect is part of the physical world.
As far as your heat transfer theory goes, when you are running in the shade or the dark, you are simply not building up near as much heat as you would be with the Sun on your face. When you stand out in the Sun, not doing any exercise at all, you can feel the Sun's radiant energy warming your body. Where to you feel hottest in the Sun? ..your head and your shoulders. Where to you sunburn? .. your head and your shoulders. When you are running in the Sun you are building up head in two places: 1) internally and 2) externally (the Sun). While heat dissipation does occur though your exposed skin's surface area, most of it builds up, and dissipates, through your upper body surfaces, specifically the head and shoulders. When you run in the shade, or dark, or with the Sun's altitude very low in the sky, the only heat that needs to be dissipated by the body is that which is being generated internally.
In the winter you wear a hat to conserve the transfer of heat from the body to the air. In the Summer you wear a hat for the opposite reason -- to reflect the build up of heat in the body coming from the Sun.
Your perception is a psychological quirk, not a physical phenomenon.