yep, essential as it seems since temperature directly impacts the speed of sound through air.
The following taken from Manchester universities (UK) website:
Sonic anemometers provide fast and accurate measurements of three dimensional wind speed and are widely used by the Centre for Atmospheric Science to make both routine wind and detailed turbulence measurements. These instruments are able to make wind speed measurements over the range 0 – 60 m/s, with a resolution of 1 cm/s at rates up to 100Hz. This speed and resolution allows turbulent structure on scales of a few cm to be resolved.
Sonic anemometers operate by measuring the time taken for a pulse of sound to travel between a pair of transducers. This time depends on the distance between the transducers, the speed of sound and the air speed along the axis of the transducers as follows:
T = L/(c+v)
Where T is time, L is the distance between transducers, c is the speed of sound, and v is the air speed along the transducer axis.
The speed of sound in air is dependant on temperature, pressure and suspended contaminants such as dust and fog. In order to obtain the air speed between the transducers, each transducer alternates as transmitter and receiver so that pulses travel in both directions between them. The air speed is calculated from the pulse times in each direction as follows:
v = 0.5L(1/t1-1/t2)
The speed of sound, from which an estimate of air temperature may be derived may be calculated from the pulse times as follows:
c = 0.5L(1/t1+1/t2)
By arranging three pairs of transducers on three different axis, three dimensional wind speed and hence direction and wind angle is obtained.
Due to the high sensitivity of sonic anemometer measurements, measurements will be affected by small flow distortions caused by the airflow past the transducers and their supporting struts. There are various designs of anemometer head which attempt to minimise such flow distortions. Additionally most manufacturers perform careful wind tunnel calibrations and automatically implement a direction dependant correction for any distortion which does occur.
Sonic anemometers are able to operate in most conditions experienced in the atmosphere, however heavy rain affects data quality from some models as water droplets on the transducers significantly effect pulse times. This problem is generally minimised by checking the signal quality of received sonic pulses and rejecting those with poor signal quality. Additionally if ice builds up on the transducers measurements are similarly affected. In order to overcome this problem some models are fitted with anti-ice heating.