The frictional drag force between separated but coupled two-dimensional electron gases of different temperatures is studied using the non-equilibrium Green function method based on the separation of center-of-mass and relative dynamics of electrons. As the mechanisms of producing the frictional force we include the direct Coulomb interaction, the interaction mediated via virtual and real TA and LA phonons, optic phonons, plasmons, and TA and LA phonon-electron collective modes. We found that, when the distance between the two electron gases is large, and at intermediate temperature where plasmons and collective modes play the most important role in the frictional drag, the possibility of having a temperature difference between two subsystems modifies greatly the transresistivity.