The heating produced by a focused laser has been shown to provide a range of manipulation tools on droplets in microfluidic situations, through the generation of thermocapillary flows whose net result is to produce a force on the drop. In particular, droplets of water in oil that are produced in microchannels can be blocked in a special test section. Here, the manipulation of the flow within the droplet is explored through spatial and temporal modulation of the laser pattern used to block the drop. When a stationary pattern of two laser spots is used, the flow preserves the mirror symmetry inside the drop, as happens in the case of two alternating spots if the frequency of the switching is higher than the response rate of the fluid. Lower frequency switching produces a time periodic flow that breaks the mirror symmetry and which leads to efficient mixing inside the droplet. The mixing that is produced by this alternating flow is studied both experimentally and using numerical simulations of particle trajectories from measured velocity fields. This mixing can be optimized for certain parameter ranges, namely by varying the distance between the spots and the forcing frequency.