  The temperature of the intergalactic medium (IGM) is an important factor in
determining the line-widths of the absorption lines in the Lyman-alpha forest.
We present a method to characterise the line-widths distribution using a
decomposition of a Lyman-alpha spectrum in terms of discrete wavelets. Such
wavelets form an orthogonal basis so the decomposition is unique. We
demonstrate using hydrodynamic simulations that the mean and dispersion of the
wavelet amplitudes is strongly correlated with both the temperature of the
absorbing gas and its dependence on the gas density. Since wavelets are also
localised in space, we are able to analyse the temperature distribution as a
function of position along the spectrum. We illustrate how this method could be
used to identify fluctuations in the IGM temperature which might result from
late reionization or local effects.
