Insufficient flexibility of existing approaches to controlling the thermal transport in atomic monolayers limits their capability for use in many applications. Here, we examine the means of electrode doping to control the thermal flux Q due to phonons propagating along the atomic monolayer. We found that the frequency of the electron-restricted phonon scattering strongly depends on the concentration n. of the electric charge carriers, established by the electric potentials applied to local gates. As a result of the electrode doping, n is increased, causing a sharp rise in both the electrical conductivity and Seebeck coefficient, while the thermal conductivity tumbles. Therefore, the effect of the thermal transistor improves the figure of merit of nanoelectronic circuits.