A population-based modelling approach was used to predict the occurrence of germination in Solanum sarrachoides (SOLSA) for different treatments. Seeds collected in Toledo (Spain) were exposed to constant temperatures, to temperatures alternating between 10 and 30°C and to gibberellins (GAs; 0, 50, 100, 150 and 1000 ppm) during a 24-h imbibition period. The following parameters were measured: base temperature (Tb), mean thermal time (θT (50)) and the standard deviation of thermal time (σθT ). The SOLSA seeds only germinated at constant temperatures when the highest GA concentration was applied. The thermal model suggests that the induction and loss of physiological dormancy following seed dispersal is achieved when temperatures vary and when a mean thermal time of 66 growing degree-days (d°C) and a Tb value of 16°C are achieved when no GA treatment was added. The concentration of GA applied under conditions of alternating temperatures has an additive effect, reducing θT (50) up to threefold, from basal level (66 d°C) to 19.40 d°C, when the 1000 ppm GA treatment was applied. In this last case, the germination was accelerated by reducing Tb to 14°C. A 5–10°C change in temperature and a range of average temperatures of 20–27.5°C promoted the germination of SOLSA seeds to the greatest extent in the absence of GA. However, these conditions are not frequently encountered in the irrigated areas of the studied region; this finding could explain the limited ability of SOLSA to expand its range within this area.