Note that this is a bumped 2013 thread.
You have something against necrophilia? 
Well, err yes. It's a sick and illegal perversion.
With regard to the thread, it's often uesful to insert a note to inform people that they may be getting into things that were resolved a decade ago rather than the specific question from the person who bumped the thread.
@OZ1LQO, I'm afraid I don't know the answer to your question but I'm sure somebody here does. I'm not sure if the Fluke 179 is one of their meters that has a publicly available service manual / schematic. It looks as if it isn't... https://eevblog.com/forum/repair/service-manual-fluke-179/
EDIT: Looking closer at the photos, it does look as if it is temperature sensing the Common jack, it's hard to think what else would need to go down there. There is a single thin bottom side track that leads from it up to the 'works' of the meter (it runs a bit close the the Volts jack and PTC surge resistor pin for my liking).
Close. It's part of the thermocouple compensation network. Here's the description from the 87V service manual, on the equivalent in that model:"Temperature
The V/Ohms input is connected the same as in mVDC to FE_O (U1 pin 19) with the
exception that U1 provides a gain of 10 to the signal. Another measurement of the
temperature of the input terminals where the thermocouple wire transitions to copper is
required to calculate the actual temperature sensed by a thermocouple. Since U1 is
controlled by the microprocessor, this measurement is done by routing two different
values of current from the U1 current source via RJT_I (U1 pin 35) to Q3 and the
resulting VBE is routed, buffered and passed to the FE_O (U1 pin 19) ready for
measurement. The reference junction temperature is calculated from these
measurements. Inductor L2 and capacitor C2 keep noise out of the measurement
circuitry. Since thermocouples are easily broken and give incorrect readings, a periodic
test of the thermocouple is required. A current from the U1 current source is routed to
ISRC (U1 pin36) and on to the thermocouple that is connected from V/Ohms to
COMMON. The resulting voltage drop across the thermocouple is connected to the U1
internal comparators and converted to a digital signal at COMP_O (U1 pin 24) ready for
evaluation by the microprocessor. "
Here's the relevant part of the circuit diagram:
