Recently, a technique has been developed whereby the radial velocity, <I>V<sub>r</sub></I>, and longitude direction, β, of propagation of an outward-moving solar transient, such as a Coronal Mass Ejection (CME), can be estimated from its track in a time-elongation map produced using Heliospheric Imager (HI) observations from a single STEREO spacecraft. The method employed, which takes advantage of an artefact of projective geometry, is based on the evaluation of the best fit of the time-elongation profile of the transient, extracted from a time-elongation map, to a set of theoretical functions corresponding to known combinations of radial velocity and direction; here we present an initial theoretical assessment of the efficacy of this technique. As the method relies on the manual selection of points along the time-elongation profile, an assessment of the accuracy with which this is feasible, is initially made. The work then presented assesses theoretically this method of recovering the velocity and propagation direction of solar transients from their time-elongation profiles using a Monte-Carlo simulation approach. In particular, we assess the range of elongations over which it is necessary to make observations in order to accurately recover these parameters. Results of the Monte-Carlo simulations suggest that it is sufficient to track a solar transient out to around 40° elongation to provide accurate estimates of its associated radial velocity and direction; the accuracy to which these parameters can be estimated for a transient tracked over a particular elongation extent is, however, sensitive to its velocity and direction relative to the Sun-Spacecraft line. These initial results suggest that this technique based on single spacecraft STEREO/HI observations could prove extremely useful in terms of providing an early warning of a CME impact on the near-Earth environment.