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Photoassociation of ultracold atoms induced by chirped picosecond pulses is analyzed in a non-perturbative treatment by following the wavepacket dynamics on the ground and excited surfaces. The initial state is described by a Boltzmann distribution of stationary continuum states. The chosen example is photoassociation of cesium atoms at temperature K from the $a^3 \Sigma_u^ + (6s,6s)$ continuum to bound levels in the external well of the 0 g -(6s + 6p 3/2) potential. We study how the modification of the pulse characteristics (carrier frequency, duration, linear chirp rate and intensity) can enhance the number of photoassociated molecules and suggest ways of optimizing the production of stable molecules.