A Coriolis principle mass flow meter is provided which is insertable into a conduit of a given diameter so as to be axially aligned with the conduit and through which flows a fluid to be measured. The flow meter includes two measuring tubes each having the same inner diameter and the same wall thickness. The two measuring tubes are coupled to an inlet manifold and an outlet manifold. The inlet and outlet manifolds are coupled to an external support tube. The flow meter also includes an internal supporting element that is parallel to the measuring tubes. Opposite ends of the internal supporting element are coupled to the inlet manifold and outlet manifold, respectively. The internal supporting element has a thermal transition resistance to the fluid which is lower than the thermal transition resistance of the external support tube to the fluid.