The aim of this paper is to set up a theoretical framework for obtaining the thermodiffusion (or Soret) coefficient of a colloid in a carrier liquid. It is first argued that the expression of the particle-current density in nonuniform temperature cannot be derived from a theoretical formula valid for an isothermal solution. Then the kinetic theory of Brownian motion is used to derive an expression for the current density properly accounting for thermodiffusion. The cases of free and interacting particles are treated, and the thermodiffusion current pertinent to an ideal solution adds up with a current driven by a temperature- and concentration-dependent potential. Accordingly, a general explicit formula for the thermodiffusion coefficient is obtained. Practical use of the framework is illustrated on simple specific models of a colloid in a solvent. Large Soret coefficients of both signs are calculated for realistic values of the physicochemical parameters, in qualitative agreement with published experimental data.