  In this note we prove two monotonicity formulas for solutions of $\Delta_H f
= c$ and $\Delta_H f - \p_t f = c$ in Carnot groups. Such formulas involve the
right-invariant \emph{carr\'e du champ} of a function and they are false for
the left-invariant one. The main results, Theorems 1.1 and 1.2, display a
resemblance with two deep monotonicity formulas respectively due to
Alt-Caffarelli-Friedman for the standard Laplacian, and to Caffarelli for the
heat equation. In connection with this aspect we ask the question whether an
"almost monotoniccity" formula be possible. In the last section we discuss the
failure of the nondecreasing monotonicity of an Almgren type functional.
