  We investigate the SU($2N$) symmetry effects with $2N>2$ on the
two-dimensional interacting Dirac fermions at finite temperatures, including
the valence-bond-solid transition, the Pomeranchuk effect, the compressibility
and the uniform spin susceptibility, by performing the determinant quantum
Monte Carlo simulations of the half-filled SU($2N$) Hubbard model on a
honeycomb lattice. The columnar valence-bond-solid (cVBS) phase only breaks the
three-fold discrete symmetry, and thus can survive at finite temperatures. The
disordered phase in the weak coupling regime is the thermal Dirac semi-metal
state, while in the strong coupling regime it is largely a Mott state in which
the cVBS order is thermally melted. The calculated entropy-temperature
relations for various values of the Hubbard interaction $U$ show that, the
Pomeranchuk effect occurs when the specific entropy is below a characteristic
value of $S^*$ --- the maximal entropy per particle from the spin channel of
local moments. The SU($2N$) symmetry enhances the Pomeranchuk effect, which
facilitates the interaction-induced adiabatic cooling. Our work sheds new light
on future explorations of novel states of matter with ultra-cold large-spin
alkaline fermions.
