I got one of these bad boys for a reason that I can't really remember, but since I have it I'll show you how to get some readings off it and we'll discuss some options of what we could do with the readings.
LM355Z Temperature Sensor
1x 1K Ohm Resistor
Step 1: : Power
Take your breadboard and your jumper wires and connect the power and ground rails, then take your LM355Z and place it on the breadboard with a 1K Ohm resistor on the middle leg.
Step 2: : Wire It Up
Take a jumper cable and connect one end (furthest away from the LM355Z) to the power cable, Jump the ground rail to the left leg of the LM355Z with one more jumper place it between the resistor and the LM355Z (Middle leg)
Step 3: : Finishing Up
Connect the power rail to the Arduino +5v line, and connect the ground rail to the Arduino Ground, then you'll want to hook the wire from the resistor to analog input 0, then follow this link. Yes it's a link to a LM355A Library but it works perfectly with the LM355Z. If you're not sure how to install libraries for your Arduino IDE, follow this helpful tutorial by LadyAda, once installed, load up the Arduino IDE and load up the example sketch and open the serial monitor and you should start seeing a data stream.
Final thoughts and ideas:
This is only a gateway to bigger and better idea's, you could create a data logger and record temperatures inside your office, fridge, coffee mug, or if keeping a temperature at a constant level is vital you could create such a system where if the temperature is off slightly it could auto correct, or even control a thermostat.
Another idea is you could hook this up to an RGB LED and have a 'quick glance' temperature mood light... The possibilities are endless.