A method of providing compensation for output data of a Coriolis flowmeter having a flow tube and a balance bar that are adapted, when in use, to be vibrated in phase opposition; said flowmeter generates Coriolis deflections of said vibrating flow tube in response to a material flow through said vibrating flow tube; said method comprising the steps of: generating a first signal representing the Coriolis deflections of said vibrating flow tube: generating a second signal representing the temperature of said flow tube; said method characterized by : outputting a third signal representing a composite temperature of a plurality of elements of said flowmeter exclusive of said flow tube, said third signal being output by a network formed by additional sensors (S2, S3, S4) coupled to said plurality of elements, said additional sensors comprising one of said additional sensors coupled to a first one of said plurality of elements, and at least another one of said additional sensors (S2, S3) coupled to a second one of said plurality of elements; wherein said network is configured to weight said third signal in favor of said first one of said plurality of elements or said second one of said plurality of elements; using said second signal and said third signal to generate information regarding a thermal state of said flow tube and said plurality of elements; using said information regarding said thermal state to compensate said output data pertaining to said material flowing through said flowmeter. generating a second signal representing the temperature of said flow tube; said method characterized by : outputting a third signal representing a composite temperature of a plurality of elements of said flowmeter exclusive of said flow tube, said third signal being output by a network formed by additional sensors (S2, S3, S4) coupled to said plurality of elements, said additional sensors comprising one of said additional sensors coupled to a first one of said plurality of elements, and at least another one of said additional sensors (S2, S3) coupled to a second one of said plurality of elements; wherein said network is configured to weight said third signal in favor of said first one of said plurality of elements or said second one of said plurality of elements; using said second signal and said third signal to generate information regarding a thermal state of said flow tube and said plurality of elements; using said information regarding said thermal state to compensate said output data pertaining to said material flowing through said flowmeter. outputting a third signal representing a composite temperature of a plurality of elements of said flowmeter exclusive of said flow tube, said third signal being output by a network formed by additional sensors (S2, S3, S4) coupled to said plurality of elements, said additional sensors comprising one of said additional sensors coupled to a first one of said plurality of elements, and at least another one of said additional sensors (S2, S3) coupled to a second one of said plurality of elements; wherein said network is configured to weight said third signal in favor of said first one of said plurality of elements or said second one of said plurality of elements; using said second signal and said third signal to generate information regarding a thermal state of said flow tube and said plurality of elements; using said information regarding said thermal state to compensate said output data pertaining to said material flowing through said flowmeter. <EOS>