Normal units is a mass flow measurement unit that uses the European temperature standard, as opposed to 'standard' units, the US mass flow units with a different temperature standard.
If you want aninferred mass flow value which is a corrected value calculated from a volumetric measurement, then yes, you need the temperature and the wherewithal to make the correction, either in the instrument or a calc in the control system.
My opinion is that for water, there is so little difference between volumetric and mass that it is not practical to worry about the difference.
For gases, the primary flow elements for DP measurement technology can be sized for design conditions that are actual flow conditions, and the transmitter's output can be called mass flow, but that assumes that the design/actual conditions are stable and consistent at all times, which in most cases is not the case. The multivariable transmitter requires and uses all three measurements, DP, temperature, and absolute pressure to correct from a volumetric flow rate to a mass flow in Standard or Normal units.
Thermal dispersion sensing technology provides a mass flow output, by design, for either gases or liquids.
Coriolis meters measure the temperature and report it, I'm actually not sure whether temperature measurement is used for the mass flow calc or not (might be used for the reported density value) or whether the vibrating tubes alone provide the mass flow value.