Failures attributed to hydrogen embrittlement are a major concern for metals so a better understanding of damage micro-mechanisms and hydrogen diffusion within the metal is needed. Local concentrations depend on transport phenomena including trapping effects, which are usually characterised by a temperature-programmed desorption method often referred to as Thermal Desorption Analysis (TDA). When the hydrogen is released from the specimen during the programmed heating, some desorption peaks are observed that are commonly related to detrapping energies by means of an analytical procedure. The limitations of this approach are revisited here and gaseous hydrogen charging at high temperatures is simulated. This popular procedure enables attaining high concentrations due to the higher solubility of hydrogen at high temperatures. However, the segregation behaviour of hydrogen into traps depends on charging time and temperature. This process and the subsequent cooling alter hydrogen distribution are numerically modelled; it is found that TDA spectra are strongly affected by the charging temperature and the charging time, both for weak and strong traps. However, the influence of ageing time at room temperature after cooling and before desorption is only appreciable for weak traps.