  In this paper, we establish gradient continuity for solutions to \[
(\partial_t - \operatorname{div}(A(x) \nabla u))^s =f,\ s \in (1/2, 1), \] when
$f$ belongs to the scaling critical function space $L(\frac{n+2}{2s-1}, 1)$.
Our main results Theorems 1.1 and 1.2 can be seen as a nonlocal generalization
of a well-known result of Stein in the context of fractional heat type
operators and sharpens some of the previous gradient continuity results which
deals with $f$ in subcritical spaces. Our proof is based on an appropriate
adaptation of compactness arguments, which has its roots in a fundamental work
of Caffarelli in [13].
