Studying changes in collagen deformation behavior at the nanoscale due to variations in mineralization and hydration is important for characterizing and developing collagen-based bio-composites. Recent studies also find that carbon nanotubes (CNTs) show promise as a reinforcing material for collagenous bio-composites. Currently, the effects of variation in mineral, water, and CNT content on collagen gap and overlap region mechanics during compression is unexplored. We use molecular dynamics simulations to investigate how variations in mineral, water, and CNT contents of collagen bio-composites in compression change their deformation behavior and thermal properties. Results indicate that variations in mineral and water content affect the collagen structure due to expansion or contraction of the gap and overlap regions. The deformation mechanisms of the gap and overlap regions also change. The presence of CNTs in non-mineralized collagen reduces the deformation of the gap region and increases the bio-composite elastic modulus to ranges comparable to mineralized collagen. The collagen/CNT bio-composites are also determined to have a higher specific heat than the studied mineralized collagen bio-composites, making them more likely to be resistant to thermal damage that could occur during implantation or functional use of a collagen collagen/CNT bio-composite biomaterial.