  In this paper we study properties of a variant of the $1/2$-caloric capacity,
called $1/2$-symmetric caloric capacity. The latter is associated
simultaneously with the $1/2$-fractional heat equation and its conjugate. We
establish its semi-additivity in $\mathbb{R}^2$ and, moreover, we compute
explicitly the $1/2$-symmetric caloric capacity of rectangles, which
illustrates its anisotropic behaviour.
