In this work, glass transition temperature of polylactide obtained over a wide range of cooling rates is investigated. The kinetics associated with the glass transition measured upon cooling and the devitrification measured upon heating are discussed. Thermal lag corrections of the glass transition temperatures are detailed. A verification of thermal lag correction values is also proposed based on structural relaxation phenomena. The glass transition is characterized in terms of fictive temperature, fragility and structural relaxation in order to discuss the intriguing non-dependency of the polylactide fictive temperatures upon cooling for high cooling rates. To our knowledge, this intriguing phenomenon is reported and detailed for the first time by fast scanning calorimetry.