Abstract <p>The control of the thermocapillary assembly of colloidal particle clusters is important for a variety of applications, including the creation of photonic crystals for microelectronics and optoelectronics, membrane formation for biotechnology, and surface cleaning for laboratory-on-chip devices. The aim of the current work is to understand the main mechanisms influencing the assembly of such clusters, which are the object of our research. Here we consider a two-dimensional mathematical model describing the transfer of particles by a thermocapillary flow in an unevenly heated cell during the evaporation of a liquid. This gave us the opportunity to study one of the main processes that triggers the formation of a particle cluster. Whether the particle will move with the flow or stop at the heater, becoming the basis for the cluster, is determined by the ratio between gravity and the drag force. The results of numerical calculations show that, for small particle concentrations, their fraction entering the cluster decreases as the volumetric heat flux density <i>Q</i> increases. The reason for this is an increase in the thermocapillary flow with an increase in the volumetric heat flux <i>Q</i>. In our conclusion, it reduces the probability of particles entering the cluster.</p>