Electrothermal motion in an aqueous solution arises from the action of an electric field on inhomogeneities in the liquid induced by temperature gradients. The temperature field can be produced by the applied electric field through Joule heating, or caused by external sources, such as strong illumination. Electrothermal flows in microsystems are usually observed at applied signal frequencies around 1 MHz and voltages around 10 V. In this work, we present self-similar solutions for the motion of an aqueous solution in a constant temperature gradient placed on top of: (a) two coplanar electrodes subjected to an a.c. potential difference, and (b) four coplanar electrodes subjected to a four-phase a.c. signal, generating a rotating field. The first case produces two-dimensional rolls whereas the second case produces a liquid whirl. Finally, we present experimental results of electrothermal liquid flows generated by alternating and rotating electric fields under strong illumination, and these experiments are compared to the analytical solutions. The induced rotating flow could be used in the mixing of analytes and of liquids in microsystems.