  We study the electric and thermal transport of the Dirac carriers in
monolayer graphene using the Boltzmann-equation approach. Motivated by recent
thermopower measurements [F. Ghahari, H.-Y.~Xie, T. Taniguchi, K. Watanabe,
M.~S.~Foster, and P.~Kim, Phys.\ Rev.\ Lett.\ {\bf 116}, 136802 (2016)], we
consider the effects of quenched disorder, Coulomb interactions, and
electron--optical-phonon scattering. Via an unbiased numerical solution to the
Boltzmann equation we calculate the electrical conductivity, thermopower, and
electronic component of the thermal conductivity, and discuss the validity of
Mott's formula and of the Wiedemann-Franz law. An analytical solution for the
disorder-only case shows that screened Coulomb impurity scattering, although
elastic, violates the Wiedemann-Franz law even at low temperature. For the
combination of carrier-carrier Coulomb and short-ranged impurity scattering, we
observe the crossover from the interaction-limited (hydrodynamic) regime to the
disorder-limited (Fermi-liquid) regime. In the former, the thermopower and the
thermal conductivity follow the results anticipated by the relativistic
hydrodynamic theory. On the other hand, we find that optical phonons become
nonnegligible at relatively low temperatures and that the induced electron
thermopower violates Mott's formula. Combining all of these scattering
mechanisms, we obtain the thermopower that quantitatively coincides with the
experimental data.
