A wide variety of climate records have revealed the existence of sudden a recurrent climatic changes. An important part of this variability might be related to transitions between stable equilibrium states of the thermohaline circulation. Here, we employ a box model of the ocean thermohaline circulation to show that in the presence of environmental fluctuations, a subthreshold periodic perturbation in the fresh water fluxes can induce quasiperiodic transitions between the stable states of the thermohaline circulation. This enhanced response occurs for a wide range of frequencies, including the Milankovic orbital forcing, and amplitudes. The mechanism that allows such response of the system under small perturbations arise from a nonlinear cooperation between the periodic perturbations and the fluctuations. Through this nonlinear mechanism, called stochastic resonance, significant climatic variability may be originated due to small perturbations enhanced by environmental noise and dynamics.