If your outside temperature gauge is not working the fault is most likely with the sensor unit. You can test both the sensor and display by connecting a 3,000 ohm resistor in place of the sensor. If the display is working properly then your gauge (with power on) will give a readout of approx. 77 degrees F (or 25C if you have a celsius gauge).
Having verified that the fault is with the sensor, you need only replace the sensor thermistor (about $5). However, M-B sells only the complete cable assembly (the sensor at the end of a long piece of wire, for about $50), which requires about 2 hours to route - hence the $200 cost. To minimize this labor some mechanics will buy the assembly, cut off the end, and splice it into the old cable. Spliced connections, particularly in the engine compartment, are not a good idea! Instead, you can easily replace the sensor yourself for $5 with no splices. Use a negative temperature coefficient (NTC) thermistor of 3k at 25C, such as Fenwal #192-302LET-A01 or Thermometrics #EC95F302W. They are readily available from any electronics supply house.
If you require more detailed procedures on testing or installation, post your questions and I'd be glad to oblige.