In the present work we study the effect of the aperiodic exchange modulation on the spin gap at finite temperature as well as the specific heat of the Kondo necklace model in two and three dimensions. For this purpose, we use 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 is also used to find the dispersion relation for the excitations of the system. The influence of the aperiodic exchange modulation on the spin gap at low temperatures is discussed in the paramagnetic phase. Moreover, we investigate the specific heat as a function of the aperiodic exchange modulation at low temperatures in two cases: above the quantum critical point i.e., along the so-called non-Fermi liquid trajectory and in the Kondo spin liquid state. We have also compared our results with previous bond operator mean-field calculations. © 2018 Elsevier B.V.