3 Wire Thermistor Wiring

I am trying to hook up a three wire thermistor to my arduino uno. It basically has two red wires, and a white one. The white one has a sticker that says PT100.

Thermistor Probe: http://www.amazon.com/gp/product/B005OUJTZI/ref=oh_details_o02_s00_i00?ie=UTF8&psc=1

I'm fairly new to arduino and electronics, though I do have over 10 years experience in software. The diagrams for hooking up the 2 wire thermistor seem pretty simple, but the few diagrams I've found for 3 wire connections, don't make mutch sense to me.

Out of curiosity, can I use it as a two wire thermistor by just using one of the red wires?

In order to measure resistance, you have to pass current through the resistor and measure the voltage drop across it. The current-carrying wires introduce their own voltage drops and make the measurement inaccurate.

The third or fourth wires in a resistive temperature sensor are there to allow you to measure the voltage drop across the element itself, in order to compensate for the voltage drop in the current carrying wires. See this summary:

How you use the sensor and its associated wires depends on how you plan to connect it to the Arduino, which you should describe. Typical connections for PT100 sensors are shown here: http://www.thermibel.be/documents/pt100/pt100-connection.xml?lang=en

I wired it up like this:

When I stick it in ice water, I get a reading on A0 of 552 (Raw). In boiling water* it goes to 608. I'm in Denver, CO, so water boils here at 202F instead of the normal 212F.

I thought I would get a bigger range between the two. I'm using this to create a PID controller for a smoker. I'll actually end up with multiple sensors to measure the following ranges:
15 to 100F - Ambient temp
150 to 210 - Internal food temp
200 to 350 - top of smoker
200 to 500? - Right near coals.

So is that a good way for wiring it up, or do I have sometihng messed up there?

That wiring is not the actual the basic idea of a Wheatstone bridge. (a missing amplifier)
You may be better off with one resitor only ! Choose a R-vaule near the PT100s resistans with temp of interest.

5V -> R -> PTC -> GND. Midpoint to Analog in

Minor point, a PT100 temp sensor should not be called a thermistor, it's a platinum variable resistance temperature sensor, most frequently called an RTD sensor. That Amazon title calling it a PT100 thermistor is in error. Thermistors are also variable resistance temperature sensors but don't use a platimum wire as the sensing element. PT100 sensors are much more expensive and accurate then most simple thermistors.