The fluid-solid phase transition behavior of nano-confined Lennard-Jones fluids as a function of temperature and degree of nanoconfinement has been studied via statistical temperature molecular dynamics (STMD). The STMD method allows the direct calculation of the density of states and thus the heat capacity with high efficiency. The fluids are simulated between parallel solid surfaces with varying pore sizes, wall-fluid interaction energies, and registry of the walls. The fluid-solid phase transition behavior has been characterized through determination of the heat capacity. The results show that for pores of ideal-spacing, the order-disorder transition temperature (T(ODT)) is reduced as the pore size increases until values consistent with that seen in a bulk system. Also, as the interaction between the wall and fluid is reduced, T(ODT) is reduced due to weak constraints from the wall. However, for non-ideal spacing pores, quite different behavior is obtained, e.g., generally T(ODT) are largely reduced, and T(ODT) is decreased as the wall constraint becomes larger. For unaligned walls (i.e., whose lattices are not in registry), the fluid-solid transition is also detected as T is reduced, indicating non-ideality in orientation of the walls does not impact the formation of a solid, but results in a slight change in T(ODT) compared to the perfectly aligned systems. The STMD method is demonstrated to be a robust way for probing the phase transitions of nanoconfined fluids systematically, enabling the future examination of the phase transition behavior of more complex fluids.