We theoretically study the self-propulsion of a laser-heated Janus particle in a near critical waterlutidine mixture, and relate its velocity vp and squirmer parameter \b{eta} to the wetting properties of its two hemispheres. For non-ionic surface forces, the particle moves the active cap ahead, except at strong driving, where a more complex behavior occurs if one of the hemispheres attracts water and the other lutidine. Both vp and \b{eta} show non-monotonic dependencies on the heating power, and may even change sign. Including the drift of the counterions due to the composition gradient, we find that a charged cap with lutidine affinity drives the particle the cap ahead, and with water affinity in the opposite direction, in agreement with experimental findings.

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