To answer it is necessary to know the dimension of particles, if they are opaque or not, their volume density, the spectrum of incident light, the density of surrounding gas,...

 Daniyar,

First you could treat each aerosol as a grey body (with non zero emissivity and albedo) and calculate the power intercepted by a single sphere. If the gas cloud is diffuse, and you can ignore scattering from one aerosol particle to another, you are lucky.

Each aerosol then warms until it reaches radiative equilibrium.

(presumably this all takes place in a vacuum - or is there a suffusing gas?)

If the cloud is optically dense, then the fun begins. You then have to account for extinction and absorption of scattered light.

How's your calculus?

(hint: Beer-Lambert)

I would first tackle this as a 1D problem. Have a column of particles - the spherical nature of the cloud doesn't appear unless the cloud is optically dense.

For particle-radiation interactions see Goody RM and Young YL, Atmopheric Radiation,  Theoretical Basis, Oxford University Press