  We analyze the partition function of the dimer model on an $\mathcal{M}
\times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley,
Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a
finite-size analysis we have found that the dimer model on such a lattice can
be described by conformal field theory having central charge $c=1$. The shift
exponent for the specific heat is found to depend on the parity of the number
of lattice sites $\mathcal{N}$ along a given lattice axis: e.g., for odd
$\mathcal{N}$ we obtain the shift exponent $\lambda=1$, while for even
$\mathcal{N}$ it is infinite ($\lambda=\infty$). In the former case, therefore,
the finite-size specific-heat pseudocritical point is size dependent, while in
the latter case, it coincides with the critical point of the thermodynamic
limit.
