Outside view of Shakespeare's window
Shakespeare saw the view from the window. He could see the sunset from that window. The sun was red, unlike daytime. It seemed like the temperature of the sun changed because red stars are relatively cool because the wave carries less energy when its wavelength is long. (E=hv) But it is unlikely for the sun to change its temperature in such a short time and periodically.
So there must be another reason. One of the difference between daytime sun and sunset sun is the light goes through the atmosphere longer than when daytime. As one can see the separation of the color in prism when white light goes through it, lights bent in a different angle determined by its wavelength. The shorter the wavelength is, the more efficiently the light is bent.
So because the sunlight travel in the atmosphere longer when
the sun sets than daytime, the light which has longer wavelength,
which is bluer lights in visible range, are scattered for a long time
and finally redder lights remain much more than bluer lights. And
that makes the sun lookes red.
Shakespeare sometimes enjoyed seeing sunset. Perhaps he knew
the sun is going to be red when it sets by considering this system,
and sometimes saw outside at that time to enjoy the red sun.