Temperature regulates the physiology and behaviour of organisms. Thus, changing temperatures induce dynamics in species interactions. Considering that consumer-resource interactions underpin ecological communities, the impacts of warming on the stability of consumer-resource interactions have been extensively studied. However, a consensus among empirically determined warming-stability relationships and a clear understanding thereof is lacking. To investigate these systematically, we propose a simplified theoretical framework that can incorporate empirical data in three steps. First, we constrain stability to intrinsic oscillations to avoid comparing disparate stability notions. Second, we reduce complexity by utilising a one-dimensional stability metric. Third, we enable the direct comparison of all data by converting all thermal dependence parameterisations into a single function, with two parameters in the exponent determining its shape. The empirical data generate four different warming-stability relationships: stability increases, decreases, is hump-shaped or U-shaped with temperature. The diversity of warming-stability relationships, though partly attributable to context-dependence, is fundamentally caused by sensitivity to two factors: how the processes within the functional response are defined and the thermal dependence of carrying capacity. Consistency across studies regarding the former and acquiring more data on the latter should help uncover systematic patterns in the thermal dependence of stability in consumer-resource interactions.