The transiting planet CoRoT-1b is thought to belong to the pM-class of planets, in which the thermal emission dominates in the optical wavelengths. We present a detection of its secondary eclipse in the CoRoT white channel data, whose response function goes from ~400 to ~1000 nm. We used two different filtering approaches, and several methods to evaluate the significance of a detection of the secondary eclipse. We detect a secondary eclipse centered within 20 min at the expected times for a circular orbit, with a depth of 0.016 ± 0.006%. The center of the eclipse is translated in a 1-σ upper limit to the planet's eccentricity of e cosω< 0.014. Under the assumption of a zero Bond Albedo and blackbody emission from the planet, it corresponds to a T_CoRoT = 2330+120-140 K. We provide the equilibrium temperatures of the planet as a function of the amount of reflected light. If the planet is in thermal equilibrium with the incident flux from the star, our results imply an inefficient transport mechanism of the flux from the day to the night sides. Based on observations obtained with CoRoT, a space project operated by the French Space Agency, CNES, with participation of the Science Programme of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany and Spain.