Femtosecond laser spectroscopies are used to examine a thymine family of systems chosen to expose the interplay between excited state deactivation and two distinct vibrational energy transfer (VET) pathways: (i) VET from the base to the deoxyribose ring; (ii) VET between neighboring units in a dinucleotide. We find that relaxation in the ground electronic state accelerates markedly as the molecular sizes increase from the nucleobase to the dinucleotide. This behavior directly reflects growth in the density of vibrational quantum states on the substituent of the base. Excited state lifetimes are studied at temperatures ranging from 100 to 300 K to characterize the thermal fluctuations that connect the Franck-Condon geometries and the conical intersections leading back to the ground state. An Arrhenius analysis yields an approximate excited state energy barrier of 13 meV in the thymine dinucleotide. In addition, we find that the transfer of vibrational energy from the base to the substituent suppresses thermal fluctuations across this energy barrier. The possibility that the solvent viscosity imposes friction on the reaction coordinate is examined by comparing thymine and adenine systems. Experiments suggest that the solvent viscosity has little effect on barrier crossing dynamics in thymine because the conical intersection is accessed through relatively small out-of-plane atomic displacements. Overall, we conclude that the transfer of vibrational quanta from thymine to the deoxyribose ring couples significantly to the internal conversion rate, whereas the neighboring unit in the dinucleotide serves as a secondary heat bath. In natural DNA, it follows that (local) thermal fluctuations in the geometries of subunits involving the base and deoxyribose ring are most important to this subpicosecond relaxation process.