We discuss a theoretical model for bidirectional cargo transport in biological cells, which is driven by teams of molecular motors and subject to thermal fluctuations. The model describes explicitly the directed motion of the molecular motors on the filament. The motor-cargo coupling is implemented via linear springs. By means of extensive Monte Carlo simulations we show that the model describes the experimentally observed regimes of anomalous diffusion, i.e. subdiffusive behavior at short times followed by superdiffusion at intermediate times. The model results indicate that subdiffuse regime is induced by thermal fluctuations while the superdiffusive motion is generated by correlations of the motors activity. We also tested the efficiency of bidirectional cargo transport in crowded areas by measuring its ability to pass barriers with increased viscosity. Our results show a remarkable gain of efficiency for high viscosities.