A control circuit determines a reception parameter for an RFID tag that is attached to an object (such as an ice pack) and then determines a frozen state of the object as a function of that reception parameter. By one approach the RFID tag provides a transmission to support the aforementioned determinations, which transmission provides no data that explicitly represents temperature. The reception parameter can comprise, for example, an indication of received signal strength. So configured, a relatively higher indication of received signal strength can serve to determine that the object is and/or remains at least substantially frozen while a relatively lower indication of received signal strength can serve to determine that the object is not at least substantially frozen.