The present study intends to examine how the viscoplasticity of the liquid affects heat transfer characteristics in a wavy channel that contains metallic porous blocks, taking into account the effect of conductive heat flow within the finite wall thickness. Additionally, the second aim of this initiative is to establish an Artificial Neural Network (ANN) framework capable of forecasting the thermohydraulic performance factor and average Nusselt number based on different combinations of thermal and rheological parameters. To examine the flow field, conductive heat flux field, conductive heat lines, average Nusselt number, and performance factor, parameters such as the Darcy number, Bingham number, and thermal conductivity of the solid wall are varied within a justified range. It turns out that the flow field is significantly influenced by its fluid’s viscoplastic characteristics, which allow the vortex to disappear at larger Bingham numbers. The average Nusselt number and performance factor show a monotonic increase with increasing Bingham numbers at higher Darcy numbers. The same exhibits a nonmonotonic tendency for lower Darcy numbers. Interestingly, the performance has been shown to have a value larger than unity, indicating that the current design has promising potential for use in applications involving thermal management of heat. The current ANN model predicts the average Nusselt number and performance factor with great precision. This endeavor represents the first exploration of how the viscoplastic properties of the liquid affect heat transfer characteristics within a wavy channel with metallic porous blocks, as well as the impact of conductive heat flow in solid walls.