We report the 75As nuclear quadrupole resonance (NQR) and specific heat measurements of the heavily hole-doped superconductor KFe2As2 (Tc = 3.5 K). The spin-lattice relaxation rate 1/T1 in the superconducting state exhibits quite gradual temperature dependence with no coherence peak below Tc. The quasi-particle specific heat C_QP/T shows small specific heat jump which is about 30% of electronic specific heat coefficient just below Tc. In addition, it suggests the existence of low-energy quasi-particle excitation at the lowest measurement temperature T = 0.4 K \simeq Tc/10. These temperature dependence of 1/T1 and C_QP/T can be explained by multiple nodal superconducting gap scenario rather than multiple fully-gapped s_\pm-wave one within simple gap analysis.
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