A heat-driven magnetization damping, that is a linear function of a temperature gradient, is predicted in antiferromagnets by considering the sublattice dynamics subjected to a heat-driven spin torque. This points to the possibility of achieving a spin torque oscillator behavior. The model is based on the magnetic Seebeck effect acting on sublattices which are exchange coupled. The heat-driven spin torque is estimated and the feasibility of detecting this effect is discussed.