We consider a representative quantum system, namely a tight-binding chain, in which an electron can tunnel to nearest-neighbour sites with equal probability. When an AC drive is applied, a fascinating phenomenon called ‘dynamic localisation occurs – the electron keeps coming back to its starting site for specific values of amplitude and frequency of the drive. While this is a zero-temperature coherent effect, we enquire whether the oscillatory field has its influence on finite temperature, incoherent, Drude-like transport and quantum diffusive motion. Our treatment of dissipative dynamics is based on the adaptation of the well-known spin-boson model under Ohmic dissipation.