  In this paper, we continue our project of defining and studying the
infinitesimal versions of the classical, real analytic, invariants of motives.
Here, we construct an infinitesimal analog of Bloch's regulator. Let $X/k$ be a
scheme of finite type over a field $k$ of characteristic 0. Suppose that
$\underline{X} \hookrightarrow X$ is a closed subscheme, smooth over $k,$ and
defined by a square-zero sheaf of ideals, which is locally free on
$\underline{X}.$ We define two regulators: $\rho_1,$ from the infinitesimal
part of the motivic cohomology ${\rm H}^2 _{M}(X,\mathbb{Q}(2))$ of $X$ to
${\rm ker}({\rm H}^{0}(X,\Omega^{1} _{X}/d\mathcal{O}_{X}) \to {\rm
H}^{0}(\underline{X},\Omega^{1}
_{\underline{X}}/d\mathcal{O}_{\underline{X}});$ and $\rho_2,$ from ${\rm
ker}(\rho_1)$ to ${\rm H}^1(X,D_{1}(\mathcal{O}_{X})),$ where
$D_{1}(\mathcal{O}_X)$ is the Zariski sheaf associated to the first
Andr\'{e}-Quillen homology. The main tool is a generalization of our additive
dilogarithm construction. Using Goodwillie's theorem, we deduce that $\rho_2$
is an isomorphism. We also reinterpret the above results in terms of the
infinitesimal Deligne-Vologodsky crystalline complex
$\mathcal{D}_{X}^{\circ}(2),$ when $X$ is smooth over the dual numbers of $k.$
