With more than 80 transits observed in the CoRoT lightcurve with a cadence of 32 s, CoRoT-Exo-2b provides an excellent case to search for the secondary eclipse of the planet, with an expected signal of less than 10-4 in relative flux. The activity of the star causes a modulation on the flux that makes the detection of this signal challenging. We describe the technique used to seek for the secondary eclipse, that leads to a tentative 2.5σ detection of a 5.5×10-5 eclipse. If the effect of the spots are not taken into account, the times of transit centers will also be affected. They could lead to an erroneous detection of periodic transit timing variations of ~20 s and with a 7.45 d period. By measuring the transit central times at different depths of the transit (transit bisectors), we show that there are no such periodic variations in the CoRoT-Exo-2b O-C residuals larger than ~10 s.