Systematic studies conducted between 15°N and 40°N over ridge segments along the slow-spreading Mid-Atlantic Ridge (MAR) have shown that segment characteristics are related to the thermal state of the segments and gradually vary with their length. This paper presents further developments of a 3-D model, based on the presence of a hot zone located under the segment centres (Gac et al. 2003), to (1) quantify the thermal structures and the geophysical signatures of segments of various lengths, considered as representative of the various MAR segments; (2) test if a simple and single model of thermal evolution can account for the characteristics of all segments and (3) explain the past evolution of the segmentation, as is observed off-axis along the MAR. The modelled thermal structure and three simulated geophysical outputs [crustal structure , along-axis variations of the earthquake maximum depth and the mantle Bouguer gravity anomalies (MBA)] are found to be directly controlled by the shape (geometry and dimensions) of the hot zone. A consistent fit between model outputs and along-axis variations of the geophysical observables over the various segments is obtained by varying solely the length of the hot zone. This result shows that segments of different length may in fact constitute the different stages of a single evolution process: the axial geophysical characteristics of the segment would progressively evolve from those of shorter segments to those of longer ones, as the hot zone lengthens along-axis. A subsequent shortening of the segment would result from a simultaneous shortening of the hot zone, segment characteristics reverting back from those of longer segments to those of shorter ones. Three geophysical fields (topography, gravity and magnetic anomalies) are simulated as the results of the thermal evolution of aligned and offset segments the length of which evolves through time. These simulations succeed in fitting observations for the entire range of observed axis offsets between adjacent MAR segments. The segment evolution produces peculiar off-axis isostatic topography and gravity anomaly (MBA), the rhomb-shaped patterns. Our simulations, which model adjacent offset segments having evolved through several cycles of lengthening and shortening, yield a good fit to the isostatic topography and MBA patterns observed in the off-axis region. Finally, the distribution of magnetization depends on the magnetic properties of each type of rocks and on the petrological structure of the lithosphere, which, in turn, results from its thermal structure and evolution. Modelled magnetic anomalies are shown to be in good agreement with off-axis observations along the N21°40' segment (TAMMAR) of the MAR.