A locally heated Janus colloid can achieve motion in a fluid through the coupling of dissolved ions and the mediums 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 Teubners 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.
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