The wet bulb temperature and the dry bulb temperature are equal when the air is satuatured with water vapor at the dry bulb temperature. For a description of the wet bulb globe thermometer and dry bulb globe thermometer, which are used to assess mean radiant temperature with and without evaporative cooling, respectively, see the ASHRAE Handbook of Fundamentals that can be download as a PDF from a number of web sites, for example, https://www.mepengineerings.com/wp-content/uploads/2020/10/2009-ashrae-handbook.pdf The definition of the heat index can be found on the Internet.
The adiabatic evaporation of water from the thermometer and the cooling effect is indicated by a "wet bulb temperature" lower than the "dry bulb temperature" in the air.The rate of evaporation from the wet bandage on the bulb, and the temperature difference between the dry bulb and wet bulb, depends on the humidity of the air. The evaporation from the wet muslin is reduced when air contains more water vapor. If the temperature difference is zero then you are at 100 percent humidity; the air is saturated and no moisture will evaporate from the wet bulb at all. Thus a relative humidity indication and wet bulb temperature is the same or lower than the dry bulb. The difference is due to evaporation which cools the wet bulb. A wet bulb thermometer measures the extent of cooling as moisture dries from a surface (evaporative cooling). The wet bulb temperature is always lower than the dry bulb temperature except when there is 100% relative humidity, making the wet bulb temperature a more accurate measurement of product temperature. The Wet Bulb Globe Temperature (WBGT) is a measure of the heat stress in direct sunlight, which takes into account: temperature, humidity, wind speed, sun angle and cloud cover (solar radiation). This differs from the heat index, which takes into consideration temperature and humidity and is calculated for shady areas. The heat index is calculated for shady areas and the wet-bulb globe temperature is calculated for areas in direct sunlight. The Wet Bulb temperature is always between the Dry Bulb temperature and the Dew Point. For the wet bulb, there is a dynamic equilibrium between heat gained because the wet bulb is cooler than the surrounding air and heat lost because of evaporation. Heat Index is another common way to measure heat stress. It is measured in the shade and combines air temperature and relative humidity to represent how hot the conditions feel at rest. The heat index does not account for the effects of wind, sunlight, radiant heat sources, or workload. Heat transfer occurs between objects by direct contact. In convection, the heat transfer takes within the fluid. In radiation, heat transfer occurs through electromagnetic waves without involving particles. The heat transfer takes place due to the difference in temperature.