In this paper, the thermal deformation response of a circular plate due to the influence of memory-dependent derivatives (MDD) is analyzed using a quasi-static approach. The top, bottom, and curved surfaces of the plate experience convective boundaries with heat flow on the outer curved radii, and additional cross-sectional heating is prescribed on the top and bottom plate surfaces. Integral transformation methods are used to solve the memory-dependent heat transfer model. Due to the complex nature of the analytical analyses, the Laplace transform is numerically inverted. The rate of change in temperature and thermal deflection is dependent on past changes, making it more suitable for studying physical problems. Numerical calculations of the obtained thermal results are performed for a copper plate and presented graphically.