More than 25 typical experimental data sets of the cold fusion phenomenon have been analyzed phenomenologically by the TNCF (trapped neutron catalyzed fusion) model based on an assumption of the quasi-stable existence of the thermal neutrons in solids with special characteristics, giving a consistent explanation of the whole data set. The densities of the assumed thermal neutron in solids have been determined in the analyses from various experimental data and were in a range of 103 to 1012 cm-3. The success of the analyses verifies the validity of the assumption of the trapped thermal neutron. Physical bases of the model were speculated, facilitating the quasi-stable existence of the thermal neutron in the crystals, thereby satisfying definite conditions.