The temperature distribution over a plate is one of the most fundamental aspects of any investigation in engineering and science, and it has implications in many different sectors. Mechanisms of heat transfer within a solid plate are of extreme importance for many fields, such as aerospace engineering, electronics, materials science, and energy systems. The ability to more accurately model and predict temperature distributions within a plate may allow for new thermal management strategy development, material selection optimization, and overall system optimization. This work investigates the numerical study of thermal behavior in rectangular plates with and without a central circular hole during steady-state heat transfer conditions. This paper aims at making a thorough analysis of the temperature distribution and heat flux on a solid plate and a hole-containing plate by changing geometric configurations and patterns of the boundary conditions, while emphasizing the impact of hole presence on the thermal performance of the plate. The presence of the aperture introduces regions of stress concentration and changes the transfer mechanism, which is the cause for localized fluctuations in temperature as well as changes in the flux of heat, too. Numerical study is made using the finite element method. Two different cases are simulated: a solid square plate with no perforation and a square plate having a central circular hole of different diameters. Several parameters, including the geometry of the plates, hole diameters, and the thermal conductivities of materials with different types of boundary conditions, affect the distribution of temperatures and heat flux in the setup. The following temperature contour and heat flux vector plots provide further insights into thermal dynamics of this setup. The results presented here are expected to improve the design and thermal performance of perforated rectangular plates, irrespective of the perforations, and hence help facilitate progress in both thermal efficiency and structural integrity.