We have studied the fluorescence emission by two-photon excitation of four dyes widely used for bioimaging studies, rhodamine 6G, fluorescein, pyrene and indo-1 at the single molecule level. The single dye molecules, spread on a glass substrate by spin coating, show a constant fluorescence output until a sudden transition to a dark state very close to the background. The bleaching time that is found to vary in the series pyrene, indo-1, fluorescein and rhodamine 6G from the fastest to the slowest one respectively, has a Gaussian distribution indicating that the observed behavior is not due to photobleaching. Moreover, the bleaching time decreases with the glass substrate temperature reaching a vanishing nonmeasurable value for a limiting temperature whose value is found in the same series as for the bleaching time, from the lowest to the highest temperature respectively. The observed bleaching shows a clear correlation to the amount of absorbed power not reirradiated as fluorescence and to the complexity of the molecule. These observations are interpreted as thermal bleaching where the temperature increase is induced by the two-photon absorption of the single dyes as confirmed also by numerical simulations.