Step 1: Process Understanding.
When a small volume of liquid evaporates into a large volume of unsaturated vapor-gas mixture, the equilibrium temperature attained is primarily the wet-bulb temperature. This occurs because the wet-bulb temperature signifies the temperature a parcel of air would reach due to evaporative cooling.
Step 2: Clarification of Alternatives.
- Dry-bulb temperature indicates the ambient air temperature and is independent of evaporation.
- Dew point is the temperature at which vapor in the air begins to condense, not the temperature associated with evaporation.
- Boiling point is the temperature at which a liquid transforms into vapor, a condition not relevant here.
Final Determination: \[ \boxed{\text{B) wet-bulb temperature}} \]