  We consider the Kuramoto model on a graph with nodes given by $n$ i.i.d.
points uniformly distributed on the $d$ dimensional torus. Two nodes are
declared neighbors if they are at distance less than $\epsilon$. We prove a
scaling limit for this model in compact time intervals as $n\to\infty$ and
$\epsilon \to 0$ such that $\epsilon^{d+2}n/\log n \to \infty$. The limiting
object is given by the heat equation. On the one hand this shows that the
nonlinearity given by the sine function disappears under this scaling and on
the other hand, provides evidence that stable equilibria of the Kuramoto model
on these graphs are, as $n\to\infty$, in correspondence with those of the heat
equation, which are explicit and given by twisted states. In view of this, we
conjecture the existence of twisted stable equilibria with high probability as
$n\to \infty$.
