Glass-transition behaviors concerning the quadruple proton/deuteron rearrangements in the crystalline p-tert-butylcalix[4]arene-toluene (BC4A.T) host-guest compound were studied by adiabatic calorimetry. The glass-transition temperatures (T-g's) of the hydrated BC4A.T-h and deuterated BC4A.T-d were found to be around 90 and 181 K, respectively. The difference of 90 K is too big to be recognized as the ordinary isotope effect, which is about S K in classical thermal activation processes. The temperature interval over which the enthalpy relaxation effect was observed was beyond 50 K, being too wide, in BC4A.T-h, while it was 20-30 K in BC4A.T-d; the latter is the one ordinarily observed in the classical processes. The associated equilibration rate in BC4A-T-h was evaluated from the enthalpy relaxation curve observed at 62 K to evidence the non-Arrhenius nature of the temperature dependence. The relaxation effect was detected even at 20 K. These are quite the same behaviors as observed in calix[4]arene, and the quantum tunneling rate in the quadruple proton rearrangement was concluded to be only a little affected by the substitution of the tert-butyl group at the para-position of each phenol moiety.