Wave instabilities of falling liquid films are crucial in many applications to enhance heat and mass transfer. Despite the importance of this issue, the interplay between the heat transfer and the wavy dynamics of falling films is still not completely understood. To get more insight, a planar laser-induced fluorescence technique has been developed for imaging the temperature distribution in the cross section of thin liquid films (approximately 0.5-1 mm thick), which are falling down an inclined heated surface. This study reports on the implementation of this imaging technique. It also discusses its advantages and limitations for the investigation of the heat transfer in the falling liquid films. Two-dimensional flow conditions and regular waves are considered for the reconstruction of a complete temperature field in the waves. Measurements provide new understanding of the wave ability to generate mixing within the film. Temperature maps reveal preferential regions where mixing occurs first, before eventually spreading to the rest of the film if the wave amplitude and the travel distance are large enough. The increase in the heat transfer coefficient is directly related to the internal mixing observed in the temperature images.