This contribution presents a mechanistic CFD analysis of unsteady laminar flow and heat transfer around a heated circular cylinder located in a simplified fin-wall-confined segment representative of compact fin and tube heat exchangers. The study focuses on flow regimes before and after the Hopf bifurcation, where a steady wake evolves into periodic vortex shedding. The objective is to determine how coherent wake structures modify the thermal boundary layer, redistribute local heat flux and affect convective heat-transfer performance in a confined three-dimensional domain. Instead of limiting the interpretation to global indicators such as drag, lift, outlet temperature or mean Nusselt number, the analysis combines time-resolved velocity and temperature fields with modal and information-theoretic diagnostics. Proper orthogonal decomposition is used to identify dominant hydrodynamic and thermal structures, while extended proper orthogonal decomposition evaluates the coupling between velocity modes and temperature fluctuations. Transfer entropy is applied as a complementary tool to examine the directionality of information transfer between velocity components and local thermal response. Preliminary results indicate that the transverse motion of the wake is more strongly linked with temperature fluctuations than the streamwise velocity deficit alone. After the onset of periodic shedding, the thermal field exhibits a frequency-locked response, suggesting repeated renewal of the near-wall thermal boundary layer. These findings show that vortex-induced heat-transfer enhancement in compact exchangers should be interpreted not only through averaged Nusselt numbers, but also through the spatial organization and temporal coherence of flow structures. The proposed framework may support the design and diagnostics of confined heat-transfer surfaces used in heat recovery, HVAC systems and other low-temperature energy technologies, where high heat-transfer density must be achieved without excessive pressure losses.