"Is all acclimatization modeled by Newton’s Law of Cooling? I have in mind things like language learning (native or foreign), and growth to adulthood. Is acclimatization the same thing as saturation? Can the logistic function be regarded as simply an upside-down version of Newton’s Law of Cooling?"

For Newton's law of cooling, you have exponential decay, $y=A+B{e}^{-<!--\; -\; -->Cx}$, where A,B,C are parameters which control the final temperature, initial temperature, and cooling rate. It satisfies the differential equation $y^{\prime }=-<!--\; -\; -->C(y-<!--\; -\; -->A)$. Note that if the initial temperature is less than the final temperature, B will be negative and we will have Newton's law of heating.
In contrast, logistic functions are modifications of $\frac{1}{1+e^{-<!--\; -\; -->x}}=1-<!--\; -\; -->\frac{e^{-<!--\; -\; -->x}}{1+e^{-<!--\; -\; -->x}}$. As x gets large, we have $1\gg <!--\; \gg \; -->e^{-<!--\; -\; -->x}$ and so $e^{-<!--\; -\; -->x}/(1+e^{-<!--\; -\; -->x})\approx <!--\; \approx \; -->e^{-<!--\; -\; -->x}$, and so for very large x, the logistic curve looks a lot like a translated and reflected exponential decay. However, this is only the long term behavior.
Overall, the logistic curve is very different from exponential decay. In particular, when x≪0, it looks like exponential growth. Indeed, logistic curves have been used to model population growth with a carrying capacity. If we assume a maximum possible population of M, then one model for such growth (which has solution a logistic curve) is given by the differential equation
$$y^{\prime }=\mathrm{\kappa <!--\; \kappa \; -->}y(M-<!--\; -\; -->y).$$
When y is very small (relative to M), this is approximately y′=κMy. When y is approximately M, this is approximately y′=κM(M−y). The first is the equation for exponential growth. The second is Newton's law of cooling. Thus, the logistic curve is interpolating between these two different phenomena.
unluckily, for populace increase or modeling gaining knowledge of or a bunch of other applications, you need to care about more than what happens at the intense ends, because the center virtually does depend. as an instance, for gaining knowledge of (just like with restrained population growth), in case you do not know tons, you can't learn a lot, and in case you know almost all there may be, you can't learn plenty, but somewhere in the middle is a candy spot, wherein enough on the way to assimilate lots (due to the fact you have got proper context), even as on the equal time, there are plenty of things still left to analyze. in case you need to version mastering, you need to keep in mind all three of those qualitatively distinctive levels, and now not just the remaining one.