Heat transfer through a laminar-wavy falling silicon oil film on a vertical plate has been investigated. The film flows down an electrically heated metal foil which delivers a constant heat flux. The temperature field at the backside of the foil is measured by a very sensitive infrared camera with high temporal resolution. Local and instantaneous heat transfer rates through the film are evaluated from the temporal development of the local wall temperature. Investigations in two-dimensional waves show the influence of the Prandtl number on the transport processes even in the laminar region. The experimental data confirm the results of numerical calculations with a spectral element method. Furthermore, the temporal averaged heat transfer has been investigated in thermally developed three-dimensional wavy films over a film Reynolds number range of 10-129 and a Prandtl number range of 10-45. The Prandtl number dependency of the heat transfer in the laminar-wavy region of the film agrees well with a recently published experimental study.