Efficient numerical algorithms are developed for use with two finite temperature semiclassical approximations to quantum dynamics both of which require trajectories generated on potentials of mean force derived from the path integral expression for the density matrix. The numerical algorithms are formed from the combination of a classical adiabatic relation similar to that used in the Car-Parrinello method and an efficient path integral molecular dynamics scheme. Results on model, an anharmonic oscillator and a realistic, fluid para-hydrogen, problem indicate that semiclassical dynamics can be obtained for virtually the same computational cost as structure and thermodynamics.