Forming of the North Atlantic multidecadal variability (MDV) remains quite enigmatic. Some studies connect the long-term North Atlantic oceanic variability to transform of the stochastic atmospheric forcing. On the other hand, the intense heat fluxes directed from ocean to atmosphere precede the large-scale positive sea surface temperature (SST) anomalies in the region (and vice versa). The last phenomenon puts some doubts on the stochastic theory and let to suggest that surface heat fluxes play just a passive role as a response to ocean dynamical processes. Analyzing a toy box model and CMIP5 control experiments we have demonstrated that observed phase shifts between SST and surface heat fluxes do not contradict a stochastic theory. The North Atlantic long-term variability can be induced via a transform of the atmospheric random forcing. However, the role of the ocean circulation processes remains crucial for the MDV forming. Specifically, the stochastic excitation of the meridional overturning circulation reproduces observed and model generated MDV. Direct atmospheric impact on SST cannot induce correctly the phase shift between input and output signals.