We analyze the flow of KCl-water solution through negatively charged reservoir-connected nanochannels under the combined effects of varying salt concentration gradients and imposed temperature gradients. In our analysis, we account for the viscosity augmentation induced by the viscoelectric effect to enhance the prediction accuracy of the underlying transport characteristics. It has been found that the viscoelectric effect substantially increases wall viscosity, owing to the stronger transverse electric field. An increase in the zeta potential leads to a monotonic rise in wall viscosity, whereas increasing the nanochannel height results in an initial increase followed by a decrease. We show that the reduction in average flow velocity due to the viscoelectric effect is attenuated and recovered by the imposed temperature gradient within its physically permissible limits between reservoirs. Our findings reveal that the average flow velocity or mass flow rate is significantly influenced by changes in the potential induced in the electric double layer (EDL) due to variations in salt concentration between reservoirs. A greater degree of EDL overlap corresponds to higher average flow velocities, particularly when the left-side reservoir contains a higher concentration of salt due to a lower temperature therein compared with the right side. As the temperature differentials between reservoirs increase, the net current exhibits an increasing trend, while the average viscosity near the wall decreases. Moreover, within a specific range of salt concentrations in the left-side reservoirs, the temperature gradient is found to significantly enhance the average flow velocity. Notably, flow reversal is anticipated at higher salt concentrations in the left-side reservoirs. We believe that the findings of this endeavor have promising implications for the advancement of nanofluidic devices leveraging thermal energy in the permissible range to regulate mass transfer for biological applications.