Many titanium alloys are age-hardened along the same lines as, say 6061 aluminum. You heat it above a certain temperature to put alloying elements into solution in the metal. (It's not molten; it's called a solid solution.) This is called solution treating. Then you quench to freeze the solution in place. Unlike carbon steel, the quenched titanium alloy is now soft. Next, you re-heat at a lower temperature for a controlled time to let some of the dissolved constituents precipitate out. This hardens the metal, and is called age hardening. The strength increases with time and temperature, peaks, then begins to fall off, until you finally reach the annealed state, and the alloy is soft again. The reason it is called age-hardening is that some alloys, like 2024 aluminum, will actually harden with age at room temperature. It just takes a long time. Most of the time, you will want to help the ageing process with heat. Books like _ASM Metals Handbook_ tell you times, temepratures, etc., for a given alloy. It won't work with all alloys or commercially pure titatnium. Beware that heat treating titanium ought to be done in a controlled-atmosphere or salt pot furnace to avoid certain issues like embrittlement from contact with air at temperature.