Temperature measurement system comprising a temperature measurement accessory for a terminal block, the temperature measurement accessory being configured to measure a temperature and to communicate said measured temperature to a processing unit, the temperature measurement accessory comprising: - a mounting mechanism configured to cooperate with the terminal block according to an insertion direction to a mounted position, the mounted mechanism comprising a heat-conductive part configured to cooperate with a current bar of the terminal block in the mounted position, - a temperature sensor attached to or located in the heat-conductive part, - a connecting assembly provided with a plug arranged to cooperate with a complementary socket of the processing unit and provided with at least one connecting wire attached at a first extremity to the temperature sensor and at a second extremity to the plug, the first extremity being extending subtantially parallel to the insertion direction or the first extremity being provided with a turning fraction that changes from a transverse to a subtantially parallel orientation to the insertion direction toward the second extremity the temperature measurement system also comprising the processing unit, wherein the processing unit comprises a measurement circuit configured to determine if the communicated temperature measured by the temperature sensor is comprised in an appropriate working range, the processing unit also comprising a warning element configured to be active when the communicated temperature is out of the appropriate working range, wherein the processing unit comprises a casing configured to be removably attached to the terminal block. - a mounting mechanism configured to cooperate with the terminal block according to an insertion direction to a mounted position, the mounted mechanism comprising a heat-conductive part configured to cooperate with a current bar of the terminal block in the mounted position, - a temperature sensor attached to or located in the heat-conductive part, - a connecting assembly provided with a plug arranged to cooperate with a complementary socket of the processing unit and provided with at least one connecting wire attached at a first extremity to the temperature sensor and at a second extremity to the plug, the first extremity being extending subtantially parallel to the insertion direction or the first extremity being provided with a turning fraction that changes from a transverse to a subtantially parallel orientation to the insertion direction toward the second extremity the temperature measurement system also comprising the processing unit, wherein the processing unit comprises a measurement circuit configured to determine if the communicated temperature measured by the temperature sensor is comprised in an appropriate working range, the processing unit also comprising a warning element configured to be active when the communicated temperature is out of the appropriate working range, wherein the processing unit comprises a casing configured to be removably attached to the terminal block. the temperature measurement system also comprising the processing unit, wherein the processing unit comprises a measurement circuit configured to determine if the communicated temperature measured by the temperature sensor is comprised in an appropriate working range, the processing unit also comprising a warning element configured to be active when the communicated temperature is out of the appropriate working range, wherein the processing unit comprises a casing configured to be removably attached to the terminal block.