This paper presents a mission analysis study for manned missions to a special class of asteroids which have been captured in a temporary geocentric orbit, as demonstrated recently by the discovery of asteroid 2006 RH120. Possible trajectories to 2006 RH120 are surveyed using a preliminary global optimization tool based on differential evolution. The minimum ΔV trajectories found by our methodology show that temporary geocentric manned missions to 2006 RH120 can be as low as 3 km/sec if launched in 2028. Parametric studies show that feasible trajectories may have a total round trip between 150 and 210 days with a stay time between 10 and 20 days. A subset of the best preliminary trajectories are validated using a higher fidelity tool capable of modeling the gravitational influence of the more relevant bodies in the solar system. A brief and preliminary discussion on the options for mission architectures that implement the proposed class of trajectories is finally presented.