Molecular junctions hold significant promise for efficient and high-power-output thermoelectric energy conversion(1-3). Recent experiments have probed the thermoelectric properties of molecular junctions(4-7). However, electrostatic control of thermoelectric properties via a gate electrode has not been possible due to technical challenges in creating temperature differentials in three-terminal devices. Here, we show that extremely large temperature gradients (exceeding 1 x 10(9) Km(-1)) can be established in nanoscale gaps bridged by molecules, while simultaneously controlling their electronic structure via a gate electrode. Using this platform, we study prototypical Au-biphenyl-4,4'-dithiol-Au and Au-fullerene-Au junctions to demonstrate that the Seebeck coefficient and the electrical conductance of molecular junctions can be simultaneously increased by electrostatic control. Moreover, from our studies of fullerene junctions, we show that thermoelectric properties can be significantly enhanced when the dominant transport orbital is located close to the chemical potential (Fermi level) of the electrodes. These results illustrate the intimate relationship between the thermoelectric properties and charge transmission characteristics of molecular junctions and should enable systematic exploration of the recent computational predictions1-3 that promise extremely efficient thermoelectric energy conversion in molecular junctions.