  Based on the recently proposed band model, the electronic specific heat of
moderately heavy electron compound YbAl$_3$ are investigated. The band term of
the Hamiltonian consists of three parts; conduction electrons described by the
nearly free electron method, localized 4f electrons of Yb ions and the
hybridization term between these electrons. Extracting several bands near the
Fermi level, we reconstruct the low-energy effective Hamiltonian in order to
consider the correlation effect, which is studied by using the self-consistent
second order perturbation theory combined with local approximation. The
temperature dependence of the specific heat $c_{\rm v}(T)$ is calculated as a
function of temperature $T$ from the numerical derivative of the internal
energy. Sommerfeld coefficient $\gamma$ is also calculated from the direct
formula. The overall structure of $c_{\rm v}(T)/T$ is in quantitative agreement
with the experimental results, which have the characteristic two-peak
structures. They originate from the correlation effect and the structure of the
non-interacting density of states, respectively. We show that our effective
Hamiltonian yielding the realistic band structure may describe quantitatively
heavy electron compounds with conduction bands composed of s- or p- electrons.
