Heterogeneity in a material’s composition can have significant impacts on the thermal response of the material system at both the fine-scale and macro-scale levels. This is especially true for porous materials, where voids in the bulk material induce thermal resistance across the system and divert heat flow within the material. Within the energy industry, understanding these effects can be critical to designing components and systems that are often subjected to high-temperature environments. The current investigation is dedicated to studying the effect of pore geometry on the effective thermal conductivity, keff, of the whole porous unit cell. To this end, a numerical assessment of non-circular porous material simulated thermal responses was performed. A set of two-dimensional, steady-state models were defined to observe the thermal effects of different pore geometries — including triangular, square, and elliptical — centered in a unit cell porous medium. The finite element method (FEM) was implemented in Fortran — using unstructured triangular meshes — to simulate the thermal response of the systems. The method of manufactured solutions (MMS) was used to perform code verification and shows that the implementation of the numerical methods is approximately second-order accurate. This paper presents a study on the effects of pore size, shape, and rotational orientation on a heterogeneous material’s dimensionless effective thermal conductivity, k*. Comparative thermal responses show the sensitivity of k* with respect to pore shape and the variable sensitivity of response to pore orientation, where pore size is a major driver in the effective thermal response.