  We investigate the quantum transport of the heat and the charge through a
quantum dot coupled to fermionic contacts under the influence of time
modulation of temperatures. We derive, within the nonequilibrium Keldysh
Green's function formalism, generic formulas for the charge and heat currents
by extending the concept of gravitational field introduced by Luttinger to the
dynamically driven system and by identifying the correct form of dynamical
contact energy. In linear response regime our formalism is validated from
satisfying the Onsager reciprocity relations and demonstrates its utility to
reveal nontrivial dynamical effects of the Coulomb interaction on charge and
energy relaxations.
