I think it is always useful to work on the log scale, no? From a purely numerical point of view? At any rate an example of where this could be useful is when computing something like
\begin{equation*}
f(t \mid 0, 1, w) = \pi\sum_{k=1}^\infty k \exp \left(\frac{-k^2\pi^2t}{2}\right)\sin(k\pi w),
\end{equation*}
as in Navarro & Fuss, 2009 and this thread here.