Audi Repair: 99 A4 Quatro 1.8 A/C, c control, myriad

Question
The outdoor temp indicator likes to shoot down to below -50F
when it gets warm and humid outside which causes the A/C to
stop working and sometimes even changes over to heat. I have
had both the outside and inside temp undicators replaced along
with a myriad of other AC related parts and recharging.

I'm really at a loss. Any suggestions.  

Answer
hello
If your car has display in cluster showing outside temp, there is two things where from A/C is taking the reading.
one from cluster and one from A/c control. I use VAG so I can see temp readings in both. (value bloks are showing all the readings). If you need to know which one , let me know. Most like it there will be a fault in one of them, but if only one of them is reading -50 and  the other is OK , I will think you have bad module.
-50 means short to ground or power. If both modules are reading the same(-50) , you have bad outside temp. sensor or shorted wires.
good luck                 pltech