The anomalous Nernst and anomalous thermal Hall effects are prominent manifestations of Berry curvature in topological magnets. However, their electrical and thermal responses are governed by different moments of the Berry curvature spectrum, making their simultaneous enhancement in a single material a significant challenge. Here, we propose a universal strategy to overcome this fundamental trade-off by exploiting the unique properties of flat bands. We demonstrate that in magnetic Weyl semimetals, suppressing band dispersion to approach a flat band concentrates the Berry curvature, leading to a synergistic enhancement of both the anomalous Nernst and thermal Hall conductivities. This mechanism is systematically validated, first through a minimal Weyl model and then in a realistic pyrochlore lattice tight-binding model. To bridge theory with experiment, we employ first-principles calculations to identify candidate materials such as ${\mathrm{ZnV}}_2{\mathrm{O}}_4$ and ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, demonstrating that their native flat bands provide a platform for strain engineering to directly control the transverse thermoelectric and thermal responses. Our work establishes flat bands as a powerful design principle for developing high-performance energy conversion and topological quantum devices.

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• Flat bands
• Hall effect
• Thermoelectric effects
• Topological materials
• Weyl semimetal
• First-principles calculations
• Tight-binding model
• Wannier function methods