We have studied experimentally the motions of liquid droplets deposited on nonwettable surfaces (silanized silicon wafers) submitted to horizontal thermal gradients delT. Systematic measurements of the drift velocity V for different droplet radii R show the following: (i) the droplets move only above a critical radius R(c) which depends on contact angle hysteresis and is inversely proportional to delT; (ii) above R(c), V increases linearly with R and delT; (iii) for large radii R (droplets flattened by gravity), V reaches a saturation value. The droplet contour is no longer circular, but presents two straight-line segments in the direction of delT. The flow patterns at the free surface of the droplets have been monitored by video recording the displacement of floating particles.