In the context of building heating systems control in office buildings, the current state-of-the-art applies either a deterministic Model Predictive Control (MPC) controller together with a nonlinear model, or a linearized model with a stochastic MPC controller. Deterministic MPC considers only one realization of the external disturbances, which can lead to a low performance solution if the forecasts of the disturbances are not accurate. Similarly, linear models are simplified representations of the building dynamics and might fail to capture some relevant behavior. In this paper, we improve upon the current literature by combining these two approaches, i.e. we adopt a nonlinear model together with a stochastic MPC controller. We consider a scenario-based MPC (SBMPC), where many realizations of the disturbances are considered, so as to include more possible future trajectories for the external disturbances. The adopted scenario generation method provides statistically significant scenarios, whereas so far in the current literature only approximate methods have been applied. Moreover, we use Modelica to obtain the model description, which allows to have a more accurate and nonlinear model. Lastly, we perform simulations comparing standard MPC vs SBMPC vs an optimal control approach with measurements of the external disturbances, and we show how our proposed scenario-based MPC controller can achieve a better performance compared to standard deterministic MPC.