In many materials, the Seebeck coefficient is not constant in temperature, and so a spatial gradient in temperature can result in a gradient in the Seebeck coefficient. If a current is driven through this gradient then a continuous version of the Peltier effect will occur. This Thomson effect was predicted and subsequently observed by Lord Kelvin in 1851. It describes the heating or cooling of a current-carrying conductor with a temperature gradient.
If a current density scriptstyle mathbf J is passed through a homogeneous conductor, the Thomson effect predicts a heat production rate scriptstyle dot q per unit volume of: