An arrangement is disclosed for measuring an environment parameter at a rotor of a rotary machine; according to some embodiments, the parameter to be measured is temperature and the machine to monitor is a turbomachine. The arrangement includes at least: a SAW or BAW device electrically coupled with an antenna, a parameter-sensitive impedance device, and two identical cables electrically coupling the SAW or BAW device respectively with the impedance device and a short-circuit or an open-circuit or a matching impedance device. The SAW or BAW device is located in a first zone of the rotor, while the parameter-sensitive impedance device is located in a second zone of the rotor remote from the first zone of the rotor. An interrogator can obtain environment parameter values by sending RF signals to the SAW or BAW device through the antenna.