The handpiece has an illumination device (2) for emitting radiation i.e. visible light, on a treatment site. A temperature sensor (4) is arranged inside the handpiece. A common electrical signal line (5) for the illumination device and the temperature sensor is provided in the handpiece. The illumination device comprises a circuit board (6), and the electrical signal line is electrically connected with the temperature sensor over the circuit board or electrical contact units provided on the circuit board. The circuit board and the temperature sensor are spaced from each other. An independent claim is also included for a medical- or dental treatment apparatus.