A statistical model for sintering of solution-processed electrically conducting nanoparticle structures is developed. The model considers thermal expansion of the particles under Joule heating as the driving force of the process. The results are used to explain the fast resistance transition observed for the recently reported rapid electrical sintering process. A comparison with experimental results shows good agreement for the kinetics of the process. A heat-equation solution is also derived for a generic geometry of a printed conductor. This provides a basis for further refinements of the model to take other driving mechanisms, such as diffusion and inter-particle forces, into account. The results of this paper help in developing quantitative understanding of the physical processes that are relevant in nanoparticle sintering.