We present a simplified, rapid, and accurate method for the measurement of the thermoelectric Thomson coefficient by the dynamical heating of a suspended wire by an alternating current. By applying a temperature gradient across the wire, we find that the response at the second harmonic of the excitation frequency is directly proportional to the Thomson coefficient. The absolute thermoelectric coefficient of a single material can therefore be extracted with high precision by using a phase sensitive detector. We test our method on platinum and nickel wires and develop both analytical and numerical models to determine the leading sources of error.