It is assumed that accreting neutron stars (NSs) in LMXBs are heated due to the compression of the existing crust by the accreted matter which gives rise to nuclear reactions in the crust. It has been shown that most of the energy is released deep in the crust by pycnonuclear reactions involving low-Z elements. We discuss if NSs in very-faint X-ray transients (VFXTs; those which have peak X-ray luminosities < 1E36 erg/s) can be used to test this model. Unfortunately we cannot conclusively answer this because of the large uncertainties in our estimates of the accretion rate history of those VFXTs, both the short-term (less than a few tens of thousands of years) and the one throughout their lifetime. The latter is important because it can be so low that the NSs might not have accreted enough matter to become massive enough that enhanced cooling processes become active. Therefore, they could be relatively warm compared to other systems for which such enhanced cooling processed have been inferred. However, the amount of matter can also not be too low because then the crust might not have been replaced significantly by accreted matter and thus a hybrid crust of partly accreted and partly original, albeit further compressed matter, might be present. This would inhibit the full range of pycnonuclear reactions to occur and thus very likely decreasing the amount of heat deposited in the crust. Furthermore, better understanding is needed how a hybrid crust affects other properties such as the thermal conductivity. We also show that some individual NS LMXBs might have hybrid crusts as well as the NSs in HMXBs. This has to be taken into account when studying the cooling properties of those systems when they are in quiescence. We show that the VFXTs are likely not the dominate transients that are associated with the brightest low-luminosity X-ray sources in globular clusters as was hypothesized.
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