<p>This study formulates a new version of a nonlinear memory kernel within the framework of the memory-dependent derivative and applies it to a two-dimensional nonlocal thermoelastic problem subjected to a heat source, using the dual phase lag model. The rationale for introducing the new version of the memory kernel is underpinned by a comprehensive literature review that brings to light the established advantages of a nonlinear quadratic kernel. A semi-analytical method is used to determine the thermophysical quantities by bringing in suitable potential functions into the analysis. The governing equations are first transformed using Laplace and Fourier integral transforms, and numerical inversion techniques are then employed to retrieve the solutions in the physical domain. Recognizing the crucial influence that kernel functions exert in the structure of memory-dependent derivative, this work undertakes a comparative analysis of two distinct generalized thermoelastic models, focusing on how variations in kernel formulations impact the resulting thermophysical behavior. The results under nonlocal influences have been examined for two distinct thermoelastic models. The influence of the memory-dependent derivative is evaluated by presenting results obtained without it and comparing them with those that incorporate its effect.</p>