In this work, the dynamic process of oil droplets impacting and migrating on structured surfaces with imposed thermal gradients was investigated. It was observed that on an isothermal smooth surface, a lubricant droplet would impact, spread to a maximum diameter, and retract; while on a non-isothermal smooth surface, an asymmetric geometrical morphology of droplet was generated, accompanying with a migration process. Relevant dimensionless parameters were employed to evaluate the dynamic process, and the physical mechanism was revealed. Decorating surfaces with convergent microgrooves pattern could not only increase the maximum spreading diameter but also accelerate the migration process. These are beneficial for the heat exchange efficiency and lubrication performances.