We modeled by kinetic Monte Carlo simulations the growth of InGaN alloys on perfectly oriented and misoriented GaN surfaces. As the growth temperature increases, we show that two phenomena occur: composition pulling along the growth direction and lateral indium rich cluster formation. We show that both phenomena have the same origin, strain, and that temperature enables these phenomena to manifest themselves in measurable quantities. Indeed, there is a continuous transition as a function of growth temperature between statistical alloys, described by a binomial distribution law, and heterogeneous layers with indium rich clusters occurring at higher growth temperatures. We quantify this transition by introducing a cluster index based on the In and Ga atom spatial distribution. We show that this cluster index increases above a given temperature, while at low temperature and, in thin layers, it is determined by surface roughness and the associated In fluctuations. Composition pulling can be observed on a larger temperature range. Composition fluctuations are thus caused by strain, and permitted by In mobility at the surface during growth at sufficiently high temperature.