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Closure models for the turbulent scalar flux are an important source of uncertainty in Reynolds-averaged-Navier-Stokes (RANS) simulations of scalar transport. This paper presents an approach to quantify this uncertainty in simulations of complex engineering flows. The approach addresses the uncertainty in modeling the pressure scrambling (PS) effect, which is the primary mechanism balancing the productions in scalar flux dynamics. Inspired by the two classical phenomenological theories of return-to-isotropy (RI) and isotropization-of-production (IP), we assume that the most likely directions of the PS term are around a fan-shaped region bounded by the RI and IP directions. Subsequently, we propose a strategy that requires two additional simulations, defining perturbations of the PS directions towards the RI and IP limits. The approach is applied to simulations of forced heat convection in a complex pin-fin array configuration, and shows favorable monotonic properties and bounding behaviors for various quantities of interest (QoIs) relevant to heat transfer. To conclude, the results are analyzed from the perspective of transverse scalar transport in a shear flow; the analysis indicates that the proposed approach is likely to exhibit monotonic behaviors in a wide range of scalar transport problems.