The dependence of free volume on temperature has been monitored in some cross-linked polyurethanes, with different chain lengths, by using positron annihilation lifetime spectroscopy (PALS). The spectra were analysed in terms of continuous distributions in order to obtain the distribution of the longest component, tau(3). The relative number and the mean size of free volume holes have been evaluated as a function of temperature : for T < T-g both the number and the volume of the holes increase; for T > T-g the number of the holes reaches a plateau while the hole volume increases significantly. The amplitude of the plateau widens with the cross-linking and the hydrogen bond interactions. At the end of the plateau the number of the holes increases more than the hole volume : the analysis of hole distribution indicates that the dispersion decreases with increasing temperature. The dispersion of the size of the nanovoids around their average values at the various temperatures has been estimated by a suitable computer code that uses a continuous sum of the decay curves with a log-normal distribution. For each sample a glass transition temperature has been estimated and compared with that obtained by d.s.c. The influence of crosslinking on the free volume is discussed.