Mathematicians (and computer scientists) view functions as maps, taking a given input to a prescribed output. The symbols are just placeholders, with no significance. This leads to notation such as $T=f(x,y)$ to describe the temperature as a function of the rectangular coordinates $x$ and $y$.
Physicists and other scientists view functions as physical quantities. $T$ is the temperature here; it's a function of location, not of any arbitrary labels used to describe the location. This is the differential geometer's notion of a scalar field on a manifold (surface). Writing something like $T=T(x,y)$ is merely a statement that, for the moment, one wishes to regard the temperature as depending on $x$ and $y$, rather than a statement that $T$ is some particular function.