For a root system R on R d and a nonnegative multiplicity function k on R, we consider the heat kernel p k (t, x, y) associated to the Dunkl-Laplacian operator ∆ k. For β ∈]0, d + 2γ[, where γ = 1 2 ∑ α∈R k(α), we study the ∆ k-Riesz kernel of index β defined by R k,β (x, y) = 1 Γ(β/2) ∫ +∞ 0 t β 2 −1 p k (t, x, y)dt and the corresponding ∆ k-Riesz potential I k,β [µ] of a Radon measure µ on R d. According to the values of β, we study the ∆ k-superharmonicity of these functions and we give some applications like the ∆ k-Riesz measure of I k,β [µ], the uniqueness principle and a pointwise Hedberg's inequality.