  A locally heated Janus colloid can achieve motion in a fluid through the
coupling of dissolved ions and the medium's polarizibility to an imposed
temperature gradient, an effect known as self-thermo(di)electrophoresis. We
numerically study the self-propulsion of such a "hot swimmer" in a monovalent
electrolyte solution using the finite-element method. The effect of
electrostatic screening for intermediate and large Debye lengths is charted and
we report on the fluid flow generated by self-thermoelectrophoresis. We obtain
excellent agreement between our analytic theory and numerical calculations in
the limit of high salinity, validating our approach. At low salt
concentrations, we consider two analytic approaches and use Teubner's integral
formalism to arrive at expressions for the speed. These expressions agree
semi-quantitatively with our numerical results for conducting swimmers,
providing further validation. Our numerical approach provides a solid framework
against the strengths and weaknesses of analytic theory can be appreciated and
which should benefit the realization and analysis of further experiments on hot
swimming.
