To determine which sensor characteristic should be prioritized for detecting very small temperature changes, it is essential to understand the different characteristics of sensors and how they are defined:

1. Accuracy: This refers to how close a sensor's measurement is to the true value. While important, accuracy is more about the correctness of the sensor readings rather than its ability to detect small changes.
2. Range: This is the span between the minimum and maximum values a sensor can measure. A wide range is useful for versatility but does not impact the sensor's ability to detect small changes.
3. Resolution: This refers to the smallest change in a measured variable that the sensor can detect. A higher resolution means the sensor can identify very slight variations in temperature, which is crucial for applications requiring the detection of minute changes.
4. Sensitivity: Sensitivity is the change in output of the sensor per unit change in the input. While this means the sensor can react significantly to changes, it does not necessarily equate to detecting smaller changes unless coupled with high resolution.

Given these definitions, the characteristic most important for detecting very small temperature changes is Resolution. This is because resolution determines the smallest detectable change, which is critical for precision in temperature measurement.

Therefore, the correct answer is Resolution.