Recent progress in data-driven turbulence modeling has shown its potential to enhance or replace traditional equation-based Reynolds-averaged Navier-Stokes (RANS) turbulence models. This work utilizes invariant neural network (NN) architectures to model Reynolds stresses and turbulent heat fluxes in forced convection flows (when the models can be decoupled). As the considered flow is statistically one dimensional, the invariant NN architecture for the Reynolds stress model reduces to the linear eddy viscosity model. To develop the data-driven models, direct numerical and RANS simulations in vertical planar channel geometry mimicking a part of the reactor downcomer are performed. Different conditions and fluids relevant to advanced reactors (sodium, lead, unitary-Prandtl-number fluid, and molten salt) constitute the training database. The models enabled accurate predictions of velocity and temperature, and compared to the baseline turbulence model with the simple gradient diffusion hypothesis, do not require tuning of the turbulent Prandtl number. The data-driven framework is implemented in the open-source graphics processing unit–accelerated spectral element solver nekRS and has shown the potential for future developments and consideration of more complex mixed convection flows.