The global surface temperature record of the last 130 years displays a stage of systematic increase on which is superimposed a small-scale variability, followed by a stage of marked slowing down. At first sight, this appears to be surprising, in view of the ongoing increase of CO 2 concentration in the atmosphere. In this work, the mechanisms that enable a dynamical system to produce such a peculiar response to an increasing control parameter are studied. The main ideas are illustrated, successively, on a linearized energy balance model subject to white or red noise, on nonlinear energy balance models admitting several stable solutions, and on a simple thermal convection model giving rise to nonperiodic (chaotic) solutions. It is shown that the action of stochastic perturbations (especially those having a relatively long correlation time), the sudden switching in the vicinity of a point of marginal stability, or finally chaotic dynamics, give rise to responses that match the temperature record. It is suggested that the variance of climatic observables is much more sensitive to the increase of a control parameter compared to the mean.