The temperature dependence of (1)H and (13)C nuclear spin-lattice relaxation rate 1/T1 has been studied in the 1.6-4.2 K temperature range in pure pyruvic acid and in pyruvic acid containing trityl radicals at a concentration of 15 mM. The temperature dependence of 1/T1 is found to follow a quadratic power law for both nuclei in the two samples. Remarkably the same temperature dependence is displayed also by the electron spin-lattice relaxation rate 1/T1e in the sample containing radicals. These results are explained by considering the effect of the structural dynamics on the relaxation rates in pyruvic acid. Dynamic nuclear polarization experiments show that below 4 K the (13)C build up rate scales with 1/T1e, in analogy to (13)C 1/T1 and consistently with a thermal mixing scenario where all the electrons are collectively involved in the dynamic nuclear polarization process and the nuclear spin reservoir is in good thermal contact with the electron spin system.