I think you are confusing the exponential function with exponential growth. The particular term in question is simply part of a larger function that describes how yeast growth rate varies with temperature, the result of which is used in the larger model which incorporates an exponential growth assumption.
No, I'm not confusing exponential growth and the exponential function. But other than that, hmmm, I think that I'd have to admit that, hmmm, maybe you're right. Now how's that for noncommittal...
However, if so, can we than perhaps agree that your exponential dependence of rate on temperature (expressed as Tmax-T) is in fact a form of the Arrhenius equation? Arrhenius equation generally applies to simple chemical reactions, but is often used as a useful, if not necessarily exact, model to describe the dependence of microbial metabolism on temperature (such as the rate of microbial degradation of contaminants in soil dependent on soil temperature).