We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions d using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in d≥3, there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In two dimensions, long-range magnetic order occurs only at T=0. The line of Néel transitions for d>2 varies with the distance to the quantum critical point QCP g as TN g ψ, where the shift exponent ψ=1/(d-1). In the paramagnetic side of the phase diagram, the spin gap behaves as Δ≈g for d≥3, consistent with the value z=1 found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for kB T Δ and along the non-Fermi-liquid trajectory. For kB T Δ, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence. © 2007 The American Physical Society.