At the boiling point of water, is an increase in the temperature a measure of heat gained?
At the boiling point of water, which at sea level is approximately 100 degree Celsius, an increase in temperature is not an indicator of the heat gained.
This is the temperature at which water changes state from liquid to gas. A gas at the same temperature as a liquid has a higher amount of energy. When water is heated at the boiling point, the extra heat added is not utilized to increase the temperature of water. Instead, it is used to convert water to water vapor (or steam). This additional heat required for the conversion is known as the heat of vaporization, and for water it is 2257 kJ/kg.
In the reverse process: when steam gets converted to liquid water, even if the temperature remains the same, steam has to lose heat for the state change to occur.
When water is at the boiling point, it is undergoing a phase change from the liquid state to the gas state (steam/vapor). During any phase change, there is no change in temperature even though more heat is being added or removed. The only way the temperature should change when water is boiling is if the pressure changes, either up or down.
Remember that heat is a measure of the total energy in the water while temperature is a measure of the average kinetic energy of all the water molecules in the container.