The formation of diatomic molecules with rotational and vibrational coherence is 
demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of 
hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, 
colliding in their electronic ground state, are excited into coherent superpositions of 
bound rovibrational levels in an electronically excited state. The rovibrational 
coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV
fluorescence. A comprehensive theoretical model based on ab initio calculations 
rationalizes the generation of coherence by Franck-Condon filtering of collision 
energies and partial waves, quantifying it in terms of an increase in quantum purity of 
the thermal ensemble. Our results open the way to coherent control of a binary reaction.