I have been diagnosing the circuit and found several interesting things. When the arduino is plugged into the 12v power supply the temps where all over the place. When I ran the arduino off my laptop USB port and the the laptop was plugged into the charger the temps fluctuated. When the laptop was running off the battery and not plugged in the temps were steady.
I did a little reading and added a .1uF capacitor to the circuit as seen in the diagram below:
As you can see I have stripped it down to just the probe circuit. I found that adding a .1uF capacitor to the circuit really reduces the fluctuation when the laptop is plugged in or the arduino is running off the 12v power supply.
I still have a little fluctuation (about 1-2 degrees) and wanted to see if there is a way I can further filter the circuit with a simple addition like the .1uF capacitor.
Thanks