High temperature+humidty and electronics
Check the datasheet of any device for electrical specifications OR the manufactures website. Sometimes information is listed by package type. There are some sensors (a lot of mems devices) that are sensitive to moisture especially before manufacture (high temp in an oven).

Most electronics operating temperature is at least 80C (again check the datasheet for max operating temperature), some parts max temp need to be derated if they consume a lot of power (like transistors). 

The biggest concert with humidity is condensation which will create shorting and corrosion. If this is a concern, you will have to protect your electronics from condensation. Most parts don't have a humidity rating but they will tell you if they do. 


  In particular I am wondering, does all wiring need to be insulated and
  do integrated circuits (such as an Arduino) need to be covered in some
  way?


Wiring should be insulated to protect against shorting. Insulating an enclosure will only protect against 


  As an example, I am using the following temperature sensor which needs
  to be wired to an Arduino. Does the temperature sensor itself have to
  be insulated as well ??


This temperature sensor needs to be exposed to the air to get a correct reading, the wires need to be insulated to protect against shorting.