Changes in the sites occupied by hydrogen in amorphous silicon with temperature are elucidated for the first time by a new muon implantation (MuSR) technique in which experimental repolarization curves are simulated by groups of theoretical curves, related to each other parametrically. After reviewing MuSR techniques based on repolarization curves, the new parametric method is introduced and applied to amorphous silicon. It reveals that the interstitial (as opposed to bonded) hydrogen moves from sites of higher to lower symmetry as the temperature is raised towards room temperature, and demonstrates significant differences in the behaviour of this interstitial atom between the pure and hydrogenated hosts. The utility of this new analytical technique is demonstrated by combining its results with those of older methods, which yields a fuller picture of hydrogen sites in amorphous silicon than that obtainable from the earlier techniques alone.