When photographers speak of colour temperature, they really mean the balance of frequencies, where reds and yellows give a warm impression and greens and blues a cold one, as I am sure you know very well. The balance of such colours in evening and morning depends both on the direction of light (horizontal light gets scattered down , which is why you can see it.) Light scattered during the day has come down at a steeper angle and through thinner layers of particles, so the red is not much affected and the blue gets scattered more, showing brighter and looking "colder". The pink of morning and evening cloudiness against the deeper blue of the sky compared with midday skies, emphasises the effect.
As for the differences between morning and evening, that is mre variable and subjective. It certainly varies with weather, season and and location. If the effect is genuine, it must be a matter of the size and concentrations of particles of dust, moisture, and ice crystals in the air. As you rightly say, light directions morning and evening do not differ in essence.
The book "Why the sky is blue" by Hoeppe gives a lot of really good stuff on such matters.
Jon