Thin liquid films serve as the paradigms of atmospheric convection, thermal convection in the Earth's mantle or turbulence in magnetohydrodynamics, thereby connecting with typical systems exhibiting turbulent mixing. In addition, recent research on colloids, interfaces and nanofluids led to advances in the development of micro-mixers (lab-on-a-chip devices). By the thermal forcing of a film, one can reach Rayleigh numbers in the turbulent regime, such that the experiment may serve as a prototype of a mixer on the basis of thermally induced turbulence in free-standing thin liquid films with thicknesses in the nanometer range. Here, the specific experimental results of a setup with a focus on the mixing statistics of a thermally driven two-dimensional thin film are presented. Our setup allows us to capture thin film interference patterns under controlled surface and atmospheric conditions. The convection is realized by placing a cooled copper rod in the center of the film. The temperature gradient between the rod and the atmosphere results in a density gradient in the liquid film, so that the varying buoyancy induces turbulent motion. The flow field is characterized by a newly developed algorithmأolor imaging velocimetry (CIV). This analysis determines not only the velocity, but also the full deformation tensor in the Lagrangian frame. On the basis of these insights, the flow in the experiment was investigated with respect to its mixing properties: we calculated the mixing efficiency and entropy of the flow scheme to sufficiently high accuracy.