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We report a detailed low-temperature thermodynamic investigation (heat capacity and magnetization) of the superconducting state of KFe 2 As 2 for H || c axis. Our measurements reveal that the properties of KFe 2 As 2 are dominated by a relatively large nodeless energy gap (∆ 0 = 1.9 k B T c ) which excludes d x 2 −y 2 symmetry. We prove the existence of several additional extremely small gaps (∆ 0 < 1.0 k B T c ) that have a profound impact on the low-temperature and low-field behavior, similar to MgB 2 , CeCoIn 5 and PrOs 4 Sb 12 . The zero-field heat capacity is analyzed in a realistic self-consistent 4-band BCS model which qualitatively reproduces the recent laser ARPES results of Okazaki et al. (Science 337 (2012) 1314). Our results show that extremely low-temperature measurements, i.e. T < 0.1 K,will be required in order to resolve the question of the existence of line nodes in this compound.

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