A theory of the temperature dependence of the shape of paramagnetic resonance lines is developed for temperatures sufficiently low to make the effects of the spin–lattice interaction and thermal expansion negligible. General expressions for the first and second moments of the line shape function as functions of the temperature are obtained, and the approximations used are discussed in detail. These expressions are applied to the case of effective spin [Formula: see text] and 1. As an illustration of the general theory numerical results are given for the paramagnetic resonance lines of nickel fluosilicate. In this case the moments become strongly temperature dependent below 10 °K.