Cold atomic clouds are promising platforms for the generation of correlated photons, although broadening mechanisms compromise their temporal coherence. In this work, we demonstrate that the geometry of the cloud can serve as a control parameter for the coherence time of the scattered light. Using polarization optics, we monitor the balance between single and multiple scattering as the cloud geometry is tuned from 3D to quasi-1D, while intensity correlation measurements are used to witness the increase in the coherence time. Our results provide a new tool to control light temporal coherence, with potential applications in quantum optics and communication.