Origami inspired structures possess attractive characteristics such as the potential to be reconfigurable and the capability to be folded into compact forms for storage. Self-folding structures, which are systems able to perform folding operations without external mechanical input, are desirable in certain circumstances such as remote applications (e.g., space applications, underwater robotics). A self-folding structural sheet consisting of two outer layers of shape memory alloy (SMA) orthogonal wire meshes separated by an inner insulating layer is considered in this work. The inner layer consists of ABS plastic columns that connect the SMA wire mesh intersections of the top and bottom layers, which are co-located and co-oriented (denoted sparse middle layer/aligned meshes design). Significant reduction on the heat transfer between the SMA layers is expected in this design compared to previously considered designs with continuous or perforated elastomeric middle layers. The geometric and power input parameters of the sparse middle layer/aligned meshes design are optimized under mechanical and thermal constraints considering finite element and reduced order analytical models. The optimal folding performance of the sparse middle layer/aligned meshes design is compared to that of the previous designs. The results show that the sparse middle layer/aligned meshes design has promising characteristics as a self-folding structural sheet and provides for tighter folds compared to the designs with elastomeric middle layers.