  In the present paper we characterize the $(1/2,+)$-caloric capacity
(associated with the $1/2$-fractional heat equation) of the usual corner-like
Cantor set of $\mathbb{R}^{n+1}$. The results obtained for the latter are
analogous to those found for Newtonian capacity. Moreover, we also characterize
the BMO and $\text{Lip}_\alpha$ variants ($0<\alpha<1$) of the $1/2$-caloric
capacity in terms of the Hausdorff contents $\mathcal{H}^n_\infty$ and
$\mathcal{H}^{n+\alpha}_\infty$ respectively.
