Two decades after the discovery of 51 Peg b, the formation processes and atmospheres of short-period gas giants remain poorly understood. Observations of eccentric systems provide key insights on those topics as they can illuminate how a planets atmosphere responds to changes in incident flux. We report here the analysis of multi-day multi-channel photometry of the eccentric (e~ 0.93) hot Jupiter HD 80606 b obtained with the Spitzer Space Telescope. The planets extreme eccentricity combined with the long coverage and exquisite precision of new periastron-passage observations allow us to break the degeneracy between the radiative and dynamical timescales of HD 80606 bs atmosphere and constrain its global thermal response. Our analysis reveals that the atmospheric layers probed heat rapidly (~4 hr radiative timescale) from $lt$500 to 1400 K as they absorb ~ 20% of the incoming stellar flux during the periastron passage, while the planets rotation period is 93$pm_{35}^{85}$ hr, which exceeds the predicted pseudo-synchronous period (40 hr).