We discuss the temperature dependence of the H-1 and C-13 nuclear spin-lattice relaxation rate 1/T-1 and dynamic nuclear polarization (DNP) performance in beta-cyclodextrins with deuterated methyl groups. It is shown that C-13 DNP-enhanced polarization is raised up to 10%. The temperature dependence of the buildup rate for nuclear spin polarization and of 1/T-1 below 4.2 K, is analyzed in the framework of the thermal mixing regime and the origin of the deviations from the theoretical behavior discussed. C-13 1/T-1 is determined at low temperature by the glassy dynamics and at high temperature by the rotational molecular motions of the deuterated methyl groups. Thanks to deuteration, relaxation times approaching 30 s are achieved at room temperature, making this material interesting for molecular imaging applications. The effect of molecular dynamics on the line width of the NMR spectra is also discussed.