Titanium-based alloys are being developed as potential high temperature shape memory alloys. This paper employed density functional theory to investigate the effect of third element on the martensitic transformation temperature of TiPd-X shape memory alloy (X=Ru, Ni, Au, Os). Their lattice parameters are well in agreement to within 3% as compared to the available experimental data. The results predicted that the 5 at. % Pt is more favourable displaying the lowest heats of formation; while the Pd addition is stable at high composition. Furthermore, their electronic properties, elastic constant and phonon dispersion curves were determined to mimic the stability of TiPd alloy for B2, L10, B19 and B19′. We found that the density of states predicted B19′ TiPd to be the most stable structures compared to B19, B2 and L10. The B2 TiPd phase is found to be mechanically unstable with respect to the monoclinic B19′ structure, consistent with the phonon dispersion curve. The temperature dependence of the B19 and L10 TiPd structures were evaluated using embedded atom method in the LAMMPS code. Their lattice parameters a and c increases with an increase in temperature in B19 and L10. We found that the L10 transforms to B2 phase at about 897 K, while B19 transformed to the B2 phase at about 1496.4K.