We investigate the nonlinear dynamics of a two-layer system consisting of a thin liquid film and an overlying gas layer driven by the Marangoni instability induced by thermal waves propagating along the solid substrate. In the case of a stationary thermal wave with sufficiently large amplitude and Marangoni number, liquid film rupture takes place with a flattish wide trough. For sufficiently small but not too small frequencies of the thermal wave, a periodic structure consisting of localized drops interconnected by thin liquid bridges emerges. This train of drops travels unidirectionally along the heated substrate following the thermal wave. For larger thermal wave frequencies, the thickness of the bridges increases enabling fluid flow between the neighboring drops. The drop-train regimes may be utilized in microfluidic applications for directed transport of liquid content enclosed in drops formed by thermocapillary forces. (c) 2014 AIP Publishing LLC.