Abstract: Motivated by a characterization of the super Ricci flow given by McCann- Topping, we introduce the notion of a super Ricci flow for a family of distance metrics defined on the disjoint union of two smooth Riemannian manifolds, $M_1$ and $M_2$, evolving by the Ricci flow. In particular, we show that this super Ricci flow property holds when the distance between points in $M_1$ and $M_2$ evolves by the heat equation. We also discuss possible applications and examples. This is joint work with Sajjad Lakzian.