Room temperature loading of metallic glasses, at stresses below the macroscopic yield stress, raises their enthalpy and causes creep. Thermal cycling of metallic glasses between room temperature and 77 K also raises their enthalpy. In both cases, the enthalpy increases are comparable to those induced by heavy plastic deformation, but, as we show, the origins must be quite different. For plastic deformation, the enthalpy increase is a fraction (<10%) of the work done (WD) (and, in this sense, the behaviour is similar to that of conventional polycrystalline metals and alloys). In contrast, the room temperature creep and the thermal cycling involve small strains well within the elastic limit; in these cases, the enthalpy increase in the glass exceeds the WD, by as much as three orders of magnitude. We argue that the increased enthalpy can arise only from an endothermic disordering process drawing heat from the surroundings. We examine the mechanisms of this process. The increased enthalpy ('stored energy') is a measure of rejuvenation and appears as an exothermic heat of relaxation on heating the glass. The profile of this heat release (the 'relaxation spectrum') is analysed for several metallic glasses subjected to various treatments. Thus, the effects of the small-strain processing (creep and thermal cycling) can be better understood, and we can explore the potential for improving properties, in particular the plasticity, of metallic glasses. Metallic glasses can exhibit a wide range of enthalpy at a given temperature, and small-strain processing may assist in accessing this for practical purposes.