  We show that paths of solutions to parabolic stochastic differential
equations have the same regularity in time as the Wiener process (as of the
current state of art). The temporal regularity is considered in the
Besov-Orlicz space $B^{1/2}_{\Phi_2,\infty}(0,T;X)$ where
$\Phi_2(x)=\exp(x^2)-1$ and $X$ is a $2$-smooth Banach space.
