This paper develops a model-based framework for the quantification and propagation of multiple uncertainty sources affecting the performance of a smart system. A smart system, in general, performs sensing, control and actuation for proper functioning of a physical subsystem (also referred to as a plant). With strong feedback coupling between several subsystems, the uncertainty in the quantities of interest (QoI) amplifies over time. The coupling in a generic smart system occurs at two levels: (1) coupling between individual subsystems (plant, cyber, actuation, sensors), and (2) coupling between nodes in a distributed computational subsystem. In this paper, a coupled smart system is decoupled and considered as a feed-forward system over time and modeled using a two-level Dynamic Bayesian Network (DBN), one at each level of coupling (between subsystems and between nodes). A DBN can aggregate uncertainty from multiple sources within a time step and across time steps. The DBN associated with a smart system can be learned using available system models, physics models and data. The proposed methodology is demonstrated for the design of a smart indoor heating system (identification of sensors and a wireless network) within cost constraints that enables room-by-room temperature control. We observe that sensor uncertainty has a higher impact on the performance of the heating system compared to the uncertainty in the wireless network.