In this talk, we will describe how we exploit the theory of Optimal Transport as a source of geometric intuition to build up the notion of Canonical Soliton. In particular, given a Ricci flow on a manifold M over a time interval I, we imagine the time parameter as an additional space direction and construct gradient Ricci solitons on the space-time M x I. As an application, we shall see how our construction encodes the monotonic quantities that underpin Perelman's work on Ricci Flow, and how old and new Harnack inequalities naturally arise as simple curvature conditions on the space-time solitons.