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.
\(F_T=\cfrac{T_aT_b}{4\pi\tau_or^2}\)
where \(T_a\) and \(T_b\) 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.
