We have measured the ultra-low-temperature thermal conductivity of heavily hole-doped Ba1-xKxFe2As2 single crystal in the doping range 0.85 < x < 0.96.A small residual linear term k0/T, comparing to that of pure KFe2As2, was found to increase with doping.This small k0/T may come from the nodal quasiparticles at the tip of the emerging off-M-centered Fermi surface pocket lobes, as recently observed by ARPES measurement (arXiv: 1308.3888).The sharp increase ofk0/T in a narrow doping range from 0.96 to 1.0 suggests that the nodal gap in heavily hole-doped Bal-xKxFe2As2 is not imposed by symmetry.It is likely an accidental nodal s-wave superconducting gap.