  We report the results of thermodynamic measurements in external magnetic
field of the cubic Ce-based cage compounds Ce$T_{2}$Cd$_{20}$ ($T$ = Ni,Pd).
Our analysis of the heat-capacity data shows that the $\Gamma_7$ doublet is the
ground state multiplet of the Ce$^{3+}$ ions. Consequently, for the $\Gamma_7$
doublet it can be theoretically shown that the Ruderman-Kittel-Kasuya-Yosida
(RKKY) interaction between the localized Ce moments mediated by the conduction
electrons, must vanish at temperatures much lower than the energy separating
the ground state doublet from the first excited $\Gamma_8$ quartet. Our
findings provide an insight as to why no long range order has been observed in
these compounds down to temperatures in the millikelvin range.
