High-refractive-index antennas with characteristic dimensions comparable to wavelength have a remarkable ability to support pronounces electric and magnetic dipole resonances. Furthermore, periodic arrangements of such resonant antennas result in narrow and strong lattice resonances facilitated by the lattice. We design iron pyrite antennas operating in the mid-infrared spectral range due to the material's low-energy bandgap and high refractive index. We utilize Kirchhoff's law, stating that emissivity and absorptance are equal to each other in equilibrium, and we apply it to improve the thermal properties of the iron pyrite metasurface. Through the excitation of collective resonances and manipulation of the antenna lattice's period, we demonstrate our capacity to control emissivity peaks. These peaks stem from the resonant excitation of electric and magnetic dipoles within proximity to the Rayleigh anomalies. In the lattice of truncated-cone antennas, we observe Rabi splitting of electric and magnetic dipole lattice resonances originating from the antennas' broken symmetry. We demonstrate that the truncated-cone antenna lattices support strong out-of-plane magnetic dipole lattice resonances at oblique incidence. We show that the truncated-cone antennas, as opposed to disks or cones, facilitate a particularly strong resonance and bound state in the continuum at the normal incidence. Our work demonstrates the effective manipulation of emissivity peaks in iron pyrite metasurfaces through controlled lattice resonances and antenna design, offering promising avenues for mid-infrared spectral engineering.