  We report a detailed low-temperature thermodynamic investigation (heat
capacity and magnetization) of the superconducting state of KFe2As2 for H || c
axis. Our measurements reveal that the properties of KFe2As2 are dominated by a
relatively large nodeless energy gap (Delta?0 = 1.9 kBTc) which excludes dx2-y2
symmetry. We prove the existence of several additional extremely small gaps
(?Delta0 < 1.0 kBTc) that have a profound impact on the low-temperature and
low-field behavior, similar to MgB2, CeCoIn5 and PrOs4Sb12. 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.
