We present theoretical and experimental investigations of thermally driven spreading films. As well as the already established regime, in which the thickness of the films is controlled by the influence of gravity and is proportional to the surface tension gradient, another regime can be obtained in which the curvature of the meniscus (out of which the film climbs) must be taken into account. Here the thickness is proportional to the square of the surface tension gradient. A systematic study of this regime has been performed for a ''free meniscus'', the curvature of which is controlled by the capillary length, and low gradients (see P. Carles, Doctoral Thesis, Paris, 1992). In this paper, we report preliminary investigations of highly curved menisci and larger gradients. New processes have to be taken into account, i.e. the change in the shape of the meniscus at high gradient and the presence of a precursor film on top of the main film at high curvatures, where this main film is especially thin and evolves slowly with time.