Arduino could do this.. Your biggest challenge is the sensors and actuator that would be part of your system.
Many commercial wind direction indicators have a rotary potentiometer. Easy to connect to +5V and an Arduino analog input.
Commercial anemometers are either pulse-output (typically hall-effect chip) or AC signal whose frequency is related to rotation speed. The pulse type can be directly interfaced to a Digital Input, but the generator type would need a comparator or operational amplifier to condition the signal back to a pulse similar to the pulse type.
An actuator to orient the wind turbine is more complex. You need some kind of position feedback, or you need to use a servomotor with a mechanical coupling like gears or cord/pulley that translated the servo motion of 180 degrees or less to 360+ degrees. Here's a servo example: http://arduino-info.wikispaces.com/SHED-Article2SOFTWARE-ServoPotPosition
(This also shows reading a potentiometer).
Temperature is pretty easy with DS18B20 sensor. Example: http://arduino-info.wikispaces.com/Brick-Temperature-DS18B20
All these rotary systems are faced with the "360 degree problem". Continuous motion with electrical connections gets complex with "Slip rings" etc. Some systems reorient after going through "zero-360" position by going "back around".
Lots of general Arduino information on the http://ArduinoInfo.Info
If you're totally new to Arduino this (under construction) may help: http://arduino-info.wikispaces.com/Arduino-What-IS-it
Let us know how the project goes along....