An oxy-fuel burner (10) with monitoring including a fuel passage (320) terminating in a fuel nozzle (322), a primary oxidant passage (330) terminating in an oxidant nozzle (333), one or more sensors including a nozzle temperature sensor (372) for sensing at least one of an oxidant nozzle temperature and a fuel nozzle temperature, and a data processor (66, 166,266) programmed to receive data from the sensors and to determine based on at least a portion of the received data the presence or absence of an abnormal burner condition including a potential partial obstruction of at least one of the primary oxidant passage (330) and the fuel passage (320) based on an increase or decrease in at least one of the oxidant nozzle temperature and the fuel nozzle temperature.