We investigate the effects of stochastic density fluctuations on the dust temperatures and the resulting infrared (IR) emission spectra of interstellar clouds as an extension of preceding investigations by Hegmann & Kegel. We consider absorption and scattering by dust grains in spherical clouds which are, on average, homogeneous but have a fluctuating density. The spatial variation of the density is described by means of a Markov process. This clump model introduces two parameters: the correlation length ln and the Gaussian width σn of the density fluctuations. As the intensity Iλ,n inherits the randomness of the density n, the ordinary radiative transfer equation has to be replaced by a generalized transfer equation of Fokker–Planck type. In the first part, we investigate the influence of our model parameters on the radiative transport in the ultraviolet (UV) and use the results to calculate the dust temperature in radiative equilibrium. Afterwards, the IR emission of the dust is modelled for the same set of clump parameters. We find that the presence of clumps decreases the effective extinction and therefore leads to substantial differences in UV illumination and dust temperatures, compared with the homogeneous case. Because of the distribution of dust temperatures, the presence of clumps also affects the IR emission and thus possible observations. In the second part, we use a fit with two blackbody spectra to determine the cloud dust mass from our synthetic IR fluxes. It is shown that in a clumpy environment the overall dust mass is generally underestimated. This effect correlates with the degree of cloud fragmentation.