Illumination of the surface of a Au(111) single-crystal electrode with short pulses of high-power laser light has been used to produce a sudden increase of its temperature. Froth the evolution of the open circuit potential during the temperature relaxation after the laser pulse, it is possible to obtain a relative measurement of the entropy of formation of the double layer. The electrode potential, where the potential transient is zero, has been identified with the potential of maximum entropy of formation of the double layer. This methodology has been applied to study the double layer formed between the Au(111) electrode and perchloric and sulfuric acid solutions. In both cases, it has been found that the potential of maximum entropy is located slightly negative to the potential of zero charge, corresponding to a negative contribution of the water-dipole moments to the electrode-solution potential drop. In addition, in the case of sulfuric acid solutions, a sharp increase of the relaxation time after the temperature change has been observed at potentials just below the phase transition to form the (root3xroot7) adlayer. This has been explained in terms of formation of sulfate islands of reduced mobility in this potential region.