The temperature evolution over the past 40 years in the Bay of Biscay (North-East Atlantic) is investigated from an in situ data analysis, completed with a satellite SST (Sea Surface Temperature) analysis over the last 20 years. The in situ dataset is an interannual version of the BoByClim climatology, covering the Bay of Biscay area with a 10-km horizontal resolution and a 5-m vertical step. The satellite dataset is the European COastral Sea Operational Observing and Forcast System Program (ECOOP) daily analysis, covering the IBIROOS (Iberian-Biscay-Irish Sea) area with a 4-km resolution. The study area (43 degrees N-50 degrees N/12 degrees W-1 degrees W) extends over the intersection of the domains covered by these two analyses. In the 0-200 m layer of this domain, a heat budget has been computed from an ocean circulation model over the period 1965-2004. Heat is essentially imported from the west by the North Atlantic Drift, then exported southward and northward, or transferred downward into deeper layers. The annual average of air-sea flux is weak, with a zero isoline crossing the domain from the northwest to the southeast. Ocean and atmosphere, forming a coupled system, have comparable contributions and may both result in a heat sink or source. At the interannual scale, variability is mainly controlled by the air-sea flux, with a secondary contribution from oceanic transport. A strong warming of similar to 0.2 degrees C/decade for the period 1965-2004 is apparent from the surface down to the 200-m depth. The decadal evolution is consistent with several analyses over the North Atlantic. Meanwhile, warming is approximately twice faster than in the whole basin. This trend is not steady, as a cooling period occurred until the early 1970's, and the temperature increase has been significantly stronger during the last 20 years (similar to 0.3 degrees C/decade between 0 and 100 m, from 1986 to 2005). The trend and the interannual variability are maximal over the northern part of the shelf. The typical duration of interannual anomalies is two years and their penetration depth is similar to 100 m, although they occasionally exceed 200 m. The interseasonal anomalies are also stronger within the mixed layer (root-mean-square, RMS = 0.6 degrees C at the surface) than below (RMS = 0.3 degrees C at 100 m). Their geographic distribution is radically different between the surface and the deep levels. A seasonal dependence of the warming rate is evident in the upper layer, as the temperature trend is stronger in summer than in winter (by a factor of 2 at the surface). Some of the potential implications for the ecosystem are discussed, particularly in terms of species distribution and dynamics of species exploited by fisheries.