That's a pretty mediocre chip to be expecting 0.1°F stability from. At 1mA 0.1°F is about 8uV. The chip has typical noise of 150uV over the bandwidth, and thermal EMFs can cause errors of some uV here and there with little trouble.
If you are running the probe at high current you might also be getting variation from bubbles and heat loss, but less from the noise and air currents. Depending on construction self-heating will be an issue even at 1mA when you are looking for +/-0.055°C.
If you have a reasonably good digital multimeter (preferably 4-wire) you can just hook it directly across the sensor and confirm one way or the other.