We report a detailed account of a pump-probe experiment on nonlinear optical phenomena in the chiral smectic A phase : opto-thermally induced director reorientation through the electroclinic effect; an optic axis rotation effect; a thermal indexing effect. In particular, we evaluate explicitly the temperature rise due to laser heating as well as the nonlinear phase shift due to the thermal indexing effect. We also show how a modeling of the interplay between the phenomena accounts well for the experimental results. Finally, we discuss the physical origin of the optic axis rotation effect.