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

 Thanks you, everybody, for your response!

2 James: we have almost black particles, and optically thin cloud (distance between particles L=0.1mm and their diameter d=1µm; the cloud itself has diameter D=10mm). In this case, according to you, I can neglect by the light extinction. Temperature in the cloud center does not exceed 350K, and at this temperature the radiation emission by the particles is also negligible in comparison with the light energy flux. Particles are tiny, so they are heated up instantly. The same for the gas within the cloud, as at our pressure 90 Pa, the heat diffusivity is very high. After all these assumptions, my model becomes very simple: Entire light energy W0 intercepted per second by particles is instantly released into the gas. Thus, I can just solve steady state heat equation with uniform heat source W0. As soon as particle fraction is small the media heat conductivity equals to the gas' one. If I am wrong somewhere, could you, please, aware me?