We compute specific heat C(T) in a strongly hole-doped Fe-based superconductor, like KFe2As2, which has only hole pockets. We model the electronic structure by a three-orbital/three-pocket model with two smaller hole pockets made out of dxz and dyz orbitals and a larger pocket made out of dxy orbital. We use as an input the experimental fact that the mass of dxy fermion is several times heavier than that of dxz/dyz fermions. We argue that the heavy dxy band gives the largest contribution to the specific heat in the normal state, but the superconducting gap on the dxy pocket is much smaller than that on dxz/dyz pockets. We argue that in this situation the jump of C(T) at Tc is determined by dxz/dyz fermions, and the ratio (Cs-Cn)/Cn is a fraction of that in a one-band BCS superconductor. At T<Tc,C(T) remains relatively flat down to some T∗, below which it rapidly drops. This behavior is consistent with the data for KFe2As2 and related materials. We use one-parameter model for the interactions and fix this only parameter by matching the experimental ratio of the gaps on the two dxz/dyz pockets. We argue that the resulting parameter-free model reproduces quantitatively the data on C(T) for KFe2As2. We further argue that the very existence of a finite T∗<Tc favors s+- gap structure over d-wave, because in the latter case T∗ would almost vanish.