Why would there be airflow from the back of a TAT probe? During walk-around checks, I occasionally find airflow coming out from the back of the TAT probes on the Airbus A320. I wonder if it's air to cool down the TATs as they are heated during flight for anti-ice purposes.

I had a look at the description and operation of the TAT probes in the AMM but I couldn't find any information about that airflow and where it comes from.
This is a so called aspirated TAT sensor, optional on the Airbus. Air is being drawn through aspirated TAT sensors to ensure that they correctly indicate the temperature even when the aircraft is not moving. 

Normal TAT sensors develop a bias when the aircraft is static. 

This video gives a nice explanation.