Context. Theoretical arguments as well as observations of young stellar objects (YSOs) support the presence of a diversified circumstellar environment. A stellar jet is thought to account for most of the stellar spin down and disk wind outflow for the observed high mass-loss rate, thus playing a major role in the launching of powerful jets. RY Tau, for instance, is an extensively studied intermediate mass pre-main sequence star. Observational data reveal a small-scale jet called micro-jet. Nevertheless, it is not clear how the micro-jet shapes the jet observed at a large scale. Aims. The goal is to investigate the spatial stability and structure of the central jet at a large scale by mixing the stellar and disk components. Methods. Two existing analytical self-similar models for the disk and the stellar winds to build the initial setups. Instead of using a polytropic equation of state, we mapped the heating and cooling sources from the analytical solutions. The heating exchange rate was controlled by two parameters, its spatial extent and its intensity. Results. The central jet and the surrounding disk are strongly affected by these two parameters. We separate the results into three categories, which show different emissivity, temperature, and velocity maps. We reached this categorization by looking at the opening angle of the stellar solution. For cylindrically, well-collimated jets, we have opening angles as low as 10° between 8 − 10 au, and for the wider jets, we can reach 30° with a morphology closer to radial solar winds. Conclusions. Our parametric study shows that the less heated the outflow is, the more collimated it appears. We also show that recollimation shocks appear consistently with UV observations in terms of temperature but not density.