The system comprises a container including a main body (3), a cover (2), an opening/closure control device for controlling the opening/closure of the container (1), a temperature sensor and an electronic board configured for collecting data acquired by said temperature sensor and for controlling a state and operation of said opening/closure control device, wherein the system further comprises a server (21) including a database; the container (1) further includes a biological sample content detector controlled by said electronic board; and the electronic board includes a communication module configured for sending to said server (21), during transport, a series of data that is at least about the content of the container (1) and the internal temperature thereof, for the storage of said series of data in the database of the server (21).