Laser ablation techniques employ fast hyperthermia mechanisms for diseased-tissue removal, characterized by high selectivity, thus preserving the surrounding healthy tissue. The associated modeling approaches are based on classical Fourier-type laws, though a limited predictivity is observed, particularly at fast time scales. Moreover, limited knowledge is available for cardiac tissue compared to radiofrequency approaches. The present work proposes a comprehensive modeling approach for the computational investigation of the key factors involved in laser-based techniques and assessing the outcomes of induced cellular thermal damage in the cardiac context. The study encompasses a comparative finite element study involving various thermal and cellular damage models incorporating optical-thermal couplings, three-state cellular death dynamics, and a second-order heat transfer formulation generalizing the classical Fourier-based heat equation. A parametric investigation of the thermal profiles shows that higher-order models accurately capture temperature dynamics and lesion formation compared with the classical Fourier-based model. The results highlight the critical role of cardiac anisotropy, influencing the shape and extent of thermal damage, while the three-state cell death model effectively describes the transition from reversible to irreversible damage. These findings demonstrate the reliability of higher-order thermal formulations, laying the basis for future investigations of arrhythmia management via in silico approaches.