Yes, warm/cool shifts have an effect on the illusion of 3dimensional depth in a still photo but that's not what most photographers are referring to when they're discussing perspective as it relates to photography. Most photographers think of perspective as a way of controlling horizontal and vertical lines and they also think of it in terms of how it effects the sense of proportion in subject matter. The latter part is what we seem to mostly be alluding to in this thread.
For example, if a beauty photographer were to choose a particular low vantage point and use a wide angle lens for a headshot of a model then the shoulder of the model could appear as large as her head in terms of proportion in the final image. But if the same photographer were to use a telephoto lens from the same vantage point while placing more distance between the camera and the model then the subject's shoulder might appear to have a more natural relationship with her head in terms of proportion in the final image. This is an example of the type of phenomenon we seem to mostly be discussing in this thread in relation to elements of perspective. I think Jack is arguing that it isn't effected by focal length as much as it is effected by distance between the subject matter and the camera lens. He's right.
That is fine. The relationship between the image size ratio of two objects is proportional to the object distance ratios--and you notice the object distance, in an absolution sense, does not have to be the same. Two bottles with one shot from ten feet and the other at twenty feet will have the same image size ratio as two bottles with one shot at one foot and the other at two feet (ratio of 1:2). Unfortunately, many people have twisted this to a simplistic answer that the only thing that defines perspective is a specific object distance, that is clearly false.
However, with your situation of shooting at a low or high angle at the model, the perspective will change with focal length. Not because the shoulder to head image ratio changes, but because the foreground to background ratio changes--the two images are not going to have the same foreground and background.
An interesting thing is that a change in focal length will still impact pespective when shooting a model straight on. If you understand two-point perspective where you use two vanishing points on a horizon to determine perspective, then you know that displacing those two points closer or further from each other will change the perspective. When you change focal length, you change magnification. The affect of the change in magnification displaces those vanishing points. So while I can use the knowledge that my object distance is going to affect the nose/ear ratio of a portrait, I can also apply my knowledge of focal length to affect the perspective.
The ideas and relationships in photography are easy. The vast interconnected number of them make it complex--and really, really interesting.