We study diffusion of charged nanoparticles in a temperature gradient and derive the corresponding Ludwig-Soret transport coefficient. Charge effects are found to enhance thermodiffusion by up to 2 orders of magnitude. We show that the inverse Soret coefficient 1/S(T) is a linear function of the colloid density n; the proportionality factor, or second virial coefficient, varies algebraically with inverse salinity, n0(-alpha); the precise value of the exponent alpha depends on the ratio of particle size and Debye length. Our findings compare favorably with experimental observations and provide, without adjustable parameters, a good fit to the data on 3-nm sodium dodecylsulfate micelles.