  Dunkl operators are differential-difference operators parametrized by a
finite reflection group and a weight function. The commutative algebra
generated by these operators generalizes the algebra of standard differential
operators and intertwines with this latter by the so-called intertwining
operator. In this paper, we give an integral representation for the operator
$V_k\circ e^{\Delta/2}$ for an arbitrary Weyl group and a large class of
regular weights $k$ containing those of non negative real parts. Our
representing measures are absolute continuous with respect the Lebesgue measure
in $\Rd$, which allows us to derive out new results about the intertwining
operator $V_k$ and the Dunkl kernel $E_k$. We show in particular that the
operator $V_k\circ e^{\Delta/2}$ extends uniquely as a bounded operator to a
large class of functions which are not necessarily differentiables. In the case
of non negative weights, this operator is shown to be positivity-preserving.
