We report on an intriguing aspect of the effects of microstructure and chemistry on thermoelectric (TE) transport properties of nanostructured Bi₂Te₃-based compounds that are associated with their topologically insulating (TI) nature. Nanograined n-type Bi₂Te₃ and Bi_1.94Nd_0.06Te₃ samples were consolidated by uniaxial hot pressing of nanoparticles (NPs) produced by solution synthesis. The grain size was controlled by changing the duration of the hot-pressing process. We found that the room-temperature values of electrical conductivity, Seebeck coefficient, and charge carrier mobility of the consolidated Bi₂Te₃ samples increase with the reduction of the average grain size. This phenomenon was observed earlier for Bi₂Se₃, which is a well-known TI material. We also found that Nd-doping reduces the electrical conductivity, Seebeck coefficient, charge carrier mobility, and thermal conductivity near room temperature (310 K). Interestingly, Nd-doping reverses the dependence of mobility on grain size compared to undoped Bi₂Te₃, which is associated with its magnetic moment. These observations can be utilized for further enhancement of the TE power factor of bulk nanograined TE materials to be applied for power generation near room temperature as well as cooling, in addition to the positive effect on reducing thermal conductivity due to phonon scattering.