The thermosensitive properties of the hydrogel poly(N-isopropylacrylamide) (pNIPAAm) together with the good mechanical properties of lyocell fibres make a combination of the two to be thought of as a smart textile. In the present study the optimal values of various parameters that control the grafting process of pNIPAAm onto lyocell fibres were determined considering the influence of the interaction between them. The copolymerization of pNIPAAm hydrogel onto lyocell fibres was performed in aqueous acidic medium using cerium(IV) as initiator. An experimental design was planned in order to study the effect of the interactions between some variables that affect the kinetics of the graft copolymerization: the cerium(IV) initiator concentration, the N-isopropylacrylamide (NIPAAm) monomer concentration and the liquor fibre-to-bath ratio. The results show that the interaction between the concentrations of NIPAAm and the initiator significantly affects the degree of grafting (DG), the optimum values being 1250 and 12.25 mmol L−1, respectively. In contrast, the liquor ratio parameter shows no significant interaction with the other two variables studied, meaning that it acts independently but showing a proportional relationship with respect to the DG obtained. In addition, the presence of pNIPAAm in the copolymer obtained was confirmed by Fourier transform infrared spectral analysis. Moreover, the water sorption capacity, depending on the temperature, of the lyocell/pNIPAAm copolymer was studied, with an increase being observed when the DG is higher than 60% and also increasing with the temperature