Vortex dynamics in 3He-B is divided by the temperature dependent damping into a high-temperature regime, where the number of vortices is conserved, and a low-temperature regime, where rapid vortex multiplication takes place in a turbulent burst. We investigate experimentally the hydrodynamic transition between these two regimes by injecting seed vortex loops into vortex-free rotating flow. The onset temperature of turbulence is dominated by the roughly exponential temperature dependence of vortex friction, but its exact value is found to depend on the injection method.