By this alone, a light beam does not disperse. From a previous post "τo The New Guy On The Block", it was proposed that hot bodies repel each other.
FT=TaTb4πτor2
where Ta and Tb are the temperatures of the two bodies involved. This is the repulsive force that is responsible for the dispersion of light.
Taken together, this would suggest that the spread of a light beam in free space is dependent on temperature. At higher temperature a beam disperse wider than when the ambient is at low temperature.