We present a procedure to determine temperature-dependent thermodynamic properties of crystalline materials from density functional theory molecular dynamics (DFT-MD). Finite temperature properties (structural, thermal, and mechanical properties) of the phases (ground state monoclinic B33, martensitic B19', and austenitic B2) of the shape memory alloy NiTi are investigated. Fluctuation formulas and numerical derivatives are used to evaluate mechanical and thermal properties. A modified version of thermodynamic upsampling is used to enable simulations with lower DFT convergence thresholds. In addition, a thermodynamic integration expression is developed to compute free energies from isobaric DFT-MD simulations that accounts for volume changes. Structural parameters, elastic constants, volume expansion, and specific heats as a function of temperature are evaluated. Phase transitions between B2 and B19' and between B19' and B33 are characterized according to their thermal energy, entropy, and free energy differences as well as their latent heats. Anharmonic effects are shown to play a large role in both stabilizing the austenite B2 phase as well as suppressing the martensitic phase transition. The quasiharmonic approximation to the free energy results in large errors in estimating the martensitic transition temperature by neglecting these large anharmonic components.