The diffusivity of hydrogen in cold-rolled pure iron is investigated using permeation and desorption methods. Electrochemical charging, electro permeation and thermal desorption spectroscopy (TDS) experiments are conducted. Firstly, the relation between the charging current and the hydrogen concentration is established. Secondly, permeation experiments are conducted at 22, 40 and 67{\deg}C to quantify the diffusivity dependence on temperature. Finally, the diffusivity is estimated by using two types of desorption experiments and Fick's law: (i) a `rest time' method, by which we measure the hydrogen content of samples held at room temperature for different times, and (ii) isothermal desorption experiments at temperatures ranging from 22 to 80{\deg}C, fitting the resulting desorption rate versus time curves. Good agreement is obtained between the isothermal desorption and permeation approaches, with observed differences discussed and rationalised. Moreover, measured diffusivity values for cold-rolled pure iron are also found to be comparable to those reported in the literature. This work demonstrates that isothermal desorption experiments are a convenient approach to determine hydrogen diffusivity over a wide range of temperatures, as facilitated by new TDS systems with fast heating rates.