Short-term instability is normally seen as an oscillation around the control point with its peaks defined in a statement. If the temperature of the bath fluid is changing during your measurements, you can't get reliable calibration results. Short-term stability is therefore absolutely crucial. Less than that can prove very frustrating. A bath's stability will vary at different temperatures.
Most baths perform best at temperatures close to ambient.
The colder or hotter the set-point, the less stability. Too many sellers give you only one spec at or near ambient. Some give a single stability spec and don't ever mention that it applies only to one temperature or a narrow range. Ask about stability over the whole range that interests you. Bath fluid also affects stability.