  We study the nature of the double-peak specific heat structure in kagome
clusters. That containing 12 spins is considered thoroughly by numerical
diagonalization. Simple models are proposed revealing the low-$T$ peak nature
at $T_l<\Delta$ ($\Delta$ is the spin gap) in this case and in those of larger
clusters studied so far. We show that the rapid increase in density of states
just above the spin gap gives rise to this peak. These models establish the
reason for the weak magnetic field sensitivity of the low-$T$ peak. Our
discussion could be appropriate for other frustrated antiferromagnetic systems
too.
