  Dirac points in two-dimensional massless Dirac fermions are topologically
protected. Although single Dirac point cannot disappear solely, a pair of two
Dirac points annihilates after merging at a time-reversal invariant momentum
(TRIM). This process triggers a topological phase transition. In this paper, we
numerically calculate the electronic specific heat ($C$) of the systems with a
honeycomb lattice and $\alpha$-(BEDT-TTF)$_2$I$_3$ in the case that two Dirac
points are moving and merging by changing the ratio of the magnitude between
the transfer integrals, which can be controlled by uniaxial pressure for
example. When two Dirac points are close to but not at TRIM, the temperature
dependence exhibits a crossover from $C\propto T^{2.0}$ (expected for separated
Dirac points) at low temperatures ($T\leq T_{\rm co}$) to $C\propto T^{1.5}$
(expected in the case of the merged Dirac points) at high temperatures ($T\geq
T_{\rm co}$). Here, $T_{\rm co}$ denotes the crossover temperature, which is
determined by the potential barrier magnitude between two Dirac points. Our
findings demonstrate that the precursor of the topological phase transition is
observed through the temperature-dependence of the electronic specific heat.
