your describing electrical faults and without a wiring diagram I'm only guessing but I'd say that because the in car display/ entertainment unit is linked to the external temperature sensor, your sensor is probably OK just that it is not been being understood by your faulty cd radio unit. I had a similar problem with my previous Peugeot 307 where the dealer said the entertainment unit was faulty and non repairable.
Sorry to say I replaced it with a more capable Kenwood unit, for a 1/4 the cost of the Peugeot replacement.
Loving my DS4 DSport - 1.6 THP160, EAT6 speed auto, Blanc Nacre
"Most Beautiful Car of the Year, 2013"