  Let $G$ be a Carnot group. We study nonlocal diffusion equations in a domain
$\Omega$ of $G$ of the form $$
u_t^\epsilon(x,t)=\int_{G}\frac{1}{\epsilon^2}K_{\epsilon}(x,y)(u^\epsilon(y,t)-u^\epsilon(x,t))\,dy,
\qquad x\in \Omega $$ with $u^\epsilon=g(x,t)$ for $x\notin\Omega$. For
appropriate rescaled kernel $K_\epsilon$ we prove that solutions $u^\epsilon$,
when $\epsilon\rightarrow0$, uniformly approximate the solution of different
local Dirichlet problem in $G$. The key tool used is the Taylor series
development for a function defined on a Carnot group.
