The paper deals with the development of convective flows in a complex system of thin liquid layers occurring under the effect of thermal load. To study this process a mathematical model which is based on the decomposition of complex problem into unitary elements (modules) with some set of rules allowing their linkage with each other was constructed. Each module represents a monotypic local model. The fluid flow and heat transfer in each of these modules are described by the Navier-Stokes and thermal conductivity equations. The boundary conditions required to solve these systems of equations are represented explicitly and written in the form of conservation laws. The numerical analysis of effect of thermal load on the characteristics of the liquid layers movement depending on the Marangoni number is carried out. It is shown that physical and thermophysical properties of liquid layers play the decisive role. It is exactly they control the convective flows in layers and determine the position and shape of interfaces. The results of model problem solutions are presented. (C) 2017 Elsevier Ltd. All rights reserved.