Sorry for digging up this thread after such a long time, but not having a definite answer to this question still brothered me. But I was finally able to find some information on the TG value:
On the website of the German Meteorological Service I found a definition of the TG value which is apparently used in the recordings of all their weather stations (not just airport stations). I only found documents in German, but no official translations.
TG = Minimum der Temperatur in 5 cm über dem Erdboden
TG = Minimum of the temperature 5 cm above the ground
It also states, that this minimum temperature is recorded for an interval between 23:51z of the previous day and 23:50z of the current day.
I guess this information could be useful in the winter time, if it is lower than the temperature temperature in 2m height. But this still wouldn't be the actual ground temperature, which could be useful to get a sense for the probable surface condition. But it is also displayed during summer time and also I am wondering if they are actually stating the minimum or maybe the current value.
It still is somewhat of an mystery to me and I am surprised that the Germans don't have any documentation about it.
I am not able to post the link to the documents, due to the 8 post rule.