  We consider how a closed Riemannian manifold and its metric tensor can be
approximately reconstructed from local distance measurements. In the part 1 of
the paper, we considered the construction of a smooth manifold in the case when
one is given the noisy distances $\tilde d(x,y)=d(x,y)+\varepsilon_{x,y}$ for
all points $x,y\in X$, where $X$ is a $\delta$-dense subset of $M$ and
$|\varepsilon_{x,y}|<\delta$. In this paper we consider a similar problem with
partial data, that is, the approximate construction of the manifold $(M,g)$
when we are given $\tilde d(x,y)$ for $x\in X$ and $y \in U\cap X$, where $U$
is an open subset of $M$. As an application, we consider the inverse problem of
determining the manifold $(M,g)$ with non-negative Ricci curvature from noisy
observations of the heat kernel $G(y,z,t)$ with separated observation points
$y\in U$ and source points $z\in M\setminus \overline U$ on the time interval
$0<t<1$.
