We report the results of infrared ( 8 \mu m ) transit and secondary eclipse photometry of the hot Neptune exoplanet , GJ 436b using Spitzer . The nearly photon-limited precision of these data allow us to measure an improved radius for the planet , and to detect the secondary eclipse . The transit ( centered at HJD = 2454280.78149 \pm 0.00016 ) shows the flat-bottomed shape typical of infrared transits , and it precisely defines the planet-to-star radius ratio ( 0.0839 \pm 0.0005 ) , independent of the stellar properties . However , we obtain the planetary radius , as well as the stellar mass and radius , by fitting to the transit curve simultaneously with an empirical mass-radius relation for M-dwarfs ( M = R ) . We find R _ { * } = M _ { * } = 0.47 \pm 0.02 in solar units , and R _ { p } = 27 , 600 \pm 1170 km ( 4.33 \pm 0.18 Earth radii ) . This radius significantly exceeds the radius of a naked ocean planet , and requires a gaseous hydrogen-helium envelope . The secondary eclipse occurs at phase 0.587 \pm 0.005 , proving a significant orbital eccentricity ( e = 0.150 \pm 0.012 ) . The amplitude of the eclipse ( 5.7 \pm 0.8 \times 10 ^ { -4 } ) indicates a brightness temperature for the planet of T = 712 \pm 36 K. If this is indicative of the planet ’ s physical temperature , it suggests the occurrence of tidal heating in the planet . An uncharacterized second planet likely provides ongoing gravitational perturbations that maintain GJ 436b ’ s orbit eccentricity over long time scales .