Context. Thermal dust emission carries information on physical conditions and dust properties in many astronomical sources. Because observations represent a sum of emission along the line of sight, their interpretation often requires radiative transfer (RT) modelling. Aims. We describe a new RT program, SOC, for computations of dust emission, and examine its performance in simulations of interstellar clouds with external and internal heating. Methods. SOC implements the Monte Carlo RT method as a parallel program for shared-memory computers. It can be used to study dust extinction, scattering, and emission. We tested SOC with realistic cloud models and examined the convergence and noise of the dust-temperature estimates and of the resulting surface-brightness maps. Results. SOC has been demonstrated to produce accurate estimates for dust scattering and for thermal dust emission. It performs well with both CPUs and GPUs, the latter providing a speed-up of processing time by up to an order of magnitude. In the test cases, accelerated lambda iterations (ALIs) improved the convergence rates but was also sensitive to Monte Carlo noise. Run-time refinement of the hierarchical-grid models did not help in reducing the run times required for a given accuracy of solution. The use of a reference field, without ALI, works more robustly, and also allows the run time to be optimised if the number of photon packages is increased only as the iterations progress. Conclusions. The use of GPUs in RT computations should be investigated further.