The normal mode spectrum for the linearized MHD equations is investigated for a simple cylindrical equilibrium. This spectrum is examined for zero and non-zero scalar resistivity. Particular attention is paid to the thermal sub-spectrum. It is shown that when resistivity is included, a ‘dissipative’ layer forms at the location of the singularity associated with the thermal continuum. For the most unstable ‘quasi-continuum modes’, the thickness of this dissipative layer is proportional to the ¼ power of the magnetic Reynolds number. This generates length scales that are of the same order of magnitude as those reported for the fine-scale structure seen in prominences. It is therefore concluded that dissipation due to resistivity may be relevant for the formation of prominence fine-scale structure.