We report an X-ray study of the composite supernova remnant 6327.1-1.1, with particular emphasis on its thermal emission. By virtue of a combined spatial and spectral analysis, we have been able to model the X-ray emission of the remnant as a sum of two components: a non-thermal component, due to the pulsar nebula and the pulsar itself, and a thermal component, of which we have analysed spectrum and morphology, after proper subtraction of the plerion. We discuss three possible interpretations of the thermal emission of 6327.1-1.1: pure Sedov expansion, expansion through a inhomogeneous medium with evaporation from ISM clouds, and radiative expansion. On the light of our new data and interpretation, we have re-derived all the physical parameters of this SNR. In the framework of Sedov or radiative expansion we derive a longer age than previously estimated (1.1 x 10(4) yr), thus not requiring a high velocity for the pulsar.