The temperature dependence of tunneling transition of the atomic particle in solids is studied near absolute zero. The different mechanisms of the temperature dependence are considered. They are the medium reorganization, the potential barrier parameters modulation, and the under-barrier friction The nonadiabatic effects are also considered. The rate constant K is described by formula ln K=ln K-0+C4T4+C5T5+C6T6+C8T8 at low temperatures. It was conducted through the comparison of theory with the experimental data from the article of Kumada [Chem. Phys. Lett. 261, 463 (1996)]. It turned out that good agreement takes place if one takes into account the quantum properties of the hydrogen crystal with the assumption of the dominated role of medium reorganization.