Low temperature behavior of the electronic specific heat C(T) in the mixed state is by the self-consistent calculation of the Eilenberger theory. In addition to the gamma T-term (gamma is a Sommerfeld coefficient), C(T) has a significant contribution of T-2-term intrinsic in the vortex state. We identify the origin of the T-2 term as (i) V-shape density of states in the vortex state and (ii) the Kramer-Pesch effect of vortex-core shrinking upon lowering T. These results for both full-gap and line-node cases reveal that the vortex core is a richer electronic structure beyond the normal core picture.