Many physical systems involve the motion of components through fluid flow and, because of the complex interdependencies between the flow and the object motion, computational techniques are often used to investigate these systems. Detailed, localized information about flow and temperature fields and other effects often requires the discretization of the moving objects in the fluid in a simulation. Remeshing is the most common method to do so. However, remeshing is restricted to triangular or tetrahedral meshes, which tend to be numerically diffuse, and remeshing can lead to significant mesh deformation and large differences in mesh size. An alternative is the overset mesh approach where a fixed background mesh is accompanied by independent "overset" meshes surrounding the moving or fixed components in the system. A refined, quadrilateral or hexahedral mesh can be maintained, moving and deforming with the fluid-solid interface as the object transits, better capturing the flow and gradients near surfaces and allowing objects to move closer together than remeshing. As interpolation schemes are used between the background and overset meshes, the mesh size distribution, the extent of the overset domain, and the interpolation type and settings affect the interpolation accuracy. These considerations are explored using the well-studied two-dimensional transient air flow over a fixed cylinder. In addition to qualitative information about the flow and temperature fields, local, transient, and time-averaged pressure coefficient and Nusselt numbers are compared as the models are altered. The study indicates the mesh distribution in the background and at the overset interfaces are critical to the proper solution interpolation as is sufficient positioning of the interpolation from any walls or high gradient locations. The information can then be considered when implementing the overset method in a computational fluid dynamics-based model.