  In this paper, we prove first-order asymptotics on a bounded open set of the
heat content when the ambient space is an ${\sf RCD}(K,N)$ space, under a
regularity condition for the boundary that we call measured interior geodesic
condition of size $\epsilon$. We carefully study such a condition, relating it
to the properties of the disintegration of the signed distance function from
$\partial \Omega$ studied by Cavalletti and Mondino.
