In this work, we examine the role of curvature and surfactant packing in controlling the structure of periodic silica/surfactant composites by driving such materials through a transformation from a hexagonal to a lamellar phase. We focus on how the interplay of desired packing and volume constraints dictates the resulting structures. In general, surfactants expand in a complex way upon heating, and this can cause a change in the optimal packing geometry. However, the presence of a rigid silica framework may prevent surfactants from reaching this preferred volume and/or curvature. Real-time in situ X-ray diffraction is used to monitor the structural evolution of these materials heated under hydrothermal treatments. Because the thermal-driven disorder of the surfactant tails drives the phase transition, we examine four types of composites with varying tail density. Ordinarily, composites consist of surfactants with one 20-carbon tail and one positively charged ammonium headgroup. Tail density is varied by replacing a small amount (0-16%) of these single-tail, single-head surfactants with single-tail, double-head 'gemini' surfactants. A greater head-tail ratio indeed produces different results, causing the phase transition to occur at higher temperatures. Using simple geometric models to gain better understanding of our experimental results, we find that, while both unfavorable curvature and limited volume may exist for the surfactants in these composites, the constrained curvature appears to be the dominant effect in driving structural rearrangement.