On mathbb R^N equipped with a normalized root system R, a multiplicity function k(alpha ) > 0, and the associated measure dw(x)=∏α∈R|⟨x,α⟩|k(α)dx,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} dw(\\mathbf{x})=\\prod _{\\alpha \\in R}|\\langle \\mathbf{x},\\alpha \\rangle |^{{k(\\alpha )}}\\, d\\mathbf{x}, \\end{aligned}$$\\end{document}let h_t(mathbf{x},mathbf{y}) denote the heat kernel of the semigroup generated by the Dunkl Laplace operator Delta _k. Let d(mathbf{x},mathbf{y})=min _{{g}in G} Vert mathbf{x}-{g}(mathbf{y})Vert , where G is the reflection group associated with R. We derive the following upper and lower bounds for h_t(mathbf{x},mathbf{y}): for all c_l>1/4 and 0<c_u<1/4 there are constants C_l,C_u>0 such that Clw(B(x,t))-1e-cld(x,y)2tΛ(x,y,t)≤ht(x,y)≤Cuw(B(x,t))-1e-cud(x,y)2tΛ(x,y,t),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} C_{l}w(B(\\mathbf {x},\\sqrt{t}))^{-1}e^{-c_{l}\\frac{d(\\mathbf {x},\\mathbf {y})^2}{t}} \\Lambda (\\mathbf{x},\\mathbf{y},t) \\le h_t(\\mathbf {x},\\mathbf {y}) \\le C_{u}w(B(\\mathbf {x},\\sqrt{t}))^{-1}e^{-c_{u}\\frac{d(\\mathbf {x},\\mathbf {y})^2}{t}} \\Lambda (\\mathbf{x},\\mathbf{y},t), \\end{aligned}$$\\end{document}where Lambda (mathbf{x},mathbf{y},t) can be expressed by means of some rational functions of Vert mathbf{x}-{g}(mathbf{y})Vert /sqrt{t}. An exact formula for Lambda (mathbf{x},mathbf{y},t) is provided.