The hypothesis that the previously discovered treelike thermal structures on water surface [Martyushev et al. "Treelike thermal structures on the water surface,"Phys. Fluids 34, 053112 (2022)] can be explained by the presence of a surface-active impurity film is being investigated. It is shown that a simple mathematical model of the film based on a free-slip condition on the water surface allows us to obtain the previously observed structures. At the same time, a no-slip boundary condition leads to results that are inconsistent with the experiment. In addition to the film, the presence of convective structures due to horizontal and vertical temperature gradients in the water layer with an aspect ratio of about 5 is important for the appearance of treelike structures on the surface.