Thermal-spin-torque (TST) in a magnetic tunnel junction (MTJ) is demonstrated by generating large temperature gradients across ultrathin MgO tunnel barriers, with this TST being significant enough to considerably affect the magnitude of the switching field of the MTJ. The origin of the TST is attributed to an asymmetry of the tunneling conductance across the zero-bias voltage of the MTJ. Through magneto-Seebeck voltage measurements, it is estimated that the charge-current that would be generated due to the temperature gradient would give rise to spin-transfer-torque (STT) that is a thousand times too small to account for the observed changes in switching fields, indicating the presence of large TST.