In the present study, the transient thermocapillary migration of a small liquid droplet on a horizontal solid surface is numerically investigated. The droplet has a large static contact angle and a high aspect ratio of the maximum height of the droplet to its footprint. The Navier-Stokes and energy equations for both the droplet and surrounding air are solved through the finite element method. The evolution of the isotherms, the flow fields and the contact angle hysteresis are presented. Two asymmetric thermocapillary vortices appear inside the droplet. The variation of the size of the thermocapillary vortex during the migration process causes the speed of the droplet to first increase significantly, and then decrease gradually to approach a constant value. The higher imposed temperature gradient causes the droplet velocity to reach its maximal value earlier and have a higher final speed. If the static contact angle of the droplet is less than (or higher) than 90°, the droplet speed is lower (or higher) since the net thermocapillary momentum in the horizontal direction is diminished (or enhanced) by the presence of capillary force. The present results for the migration velocity and the contact angle hysteresis for a squalane droplet are also in good agreement with the previous experimental results.