The phase stability of vanadium metal and vanadium-chromium alloys at high temperatures and pressures is explored by means of first-principles electronic-structure calculations. Utilizing the self-consistent ab initio lattice dynamics approach in conjunction with density-functional theory, we show that pressure-induced mechanical instability of body-centered cubic vanadium metal, which results in formation of a rhombohedral phase at around 60--70 GPa at room temperature, will survive significant heating and compression. Furthermore, alloying with chromium decreases the temperature at which stabilization of the body-centered cubic phase occurs at elevated pressure.