Accurately determining the operating conditions of thermal systems with limited measurements is a critical challenge in convection-dominated problems of interest for nuclear engineering applications. Because of the complexity of these phenomena, existing research has often relied on data-driven reconstruction of physical quantities. In this work, instead of using a data-driven approach, which usually lacks interpretability, we focus on a physics-based inverse problem to estimate unknown causes from available observations. We address the problem of estimating operating conditions (such as heat source intensity and flow rate) in a steady-state turbulent forced convection system from a limited number of temperature measurements. Based on a forward model with quantified uncertainty, we employed Newton’s method to estimate unknown parameters and incorporated uncertainty quantification. The uncertainty analysis addresses the impact of measurement uncertainty and errors in closure relationships. The identified uncertainties provide insights into their mitigation and inform experimental design. The structured approach to inverse analysis enables accurate estimation with minimal sensor data, as shown in this specific example. The analysis will contribute to the development of advanced sparse sensing techniques, with potential implications for broader industrial and environmental applications.