In this talk, we provide a numerical study of the recently developed generalised temperature-dependent Smoluchowski equations. To solve the new complex system, we adapt and improve the low-rank approach of solving large ODE systems. This allows us to quickly find approximate solutions for generalised systems of Smoluchowski equations even when the collision kernels change during aggregation. Our results confirm the analytical predictions of the temperature-dependent scaling, including analytically obtained scaling parameters. We also use a special type of Monte-Carlo simulations (temperature-dependent Monte-Carlo) to plot a phase diagram for different values of aggregation probability. We observe both temperature decrease and temperature increase scaling, as well as find more interesting behaviours at small system times.