  We provide an analytical description of the line broadening of HI absorbers
in the Lyman-alpha forest resulting from Doppler broadening and Jeans
smoothing. We demonstrate that our relation captures the dependence of the
line-width on column density for narrow lines in z~3 mock spectra remarkably
well. Broad lines at a given column density arise when the underlying density
structure is more complex, and such clustering is not captured by our model.
Our understanding of the line broadening opens the way to a new method to
characterise the thermal state of the intergalactic medium and to determine the
sizes of the absorbing structures.
