Spray chamber: Issues related to air cooling and humidification treatment

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Air treatment is carried out by using a spray chamber to cool and humidify the air. When the temperature of the water being sprayed, that is, the temperature at the nozzle outlet, equals the dry-bulb temperature of the air entering the treatment system, why is it considered isothermal humidification? The book states that: \"The saturated vapor pressure of the air layer on the surface of the water droplets is greater than the vapor pressure of water in the air; therefore, water vapor will continuously evaporate into the air, humidifying it and providing the corresponding latent heat.\" The latent heat of the air will increase, as will its moisture content and specific enthalpy, while the temperature remains unchanged. In this process, it is referred to as a \"constant-temperature humidification process.\" As stated in the 113-page book \"Air Conditioning Engineering,\" edited by Huang Xiang and reviewed by Wang Tianfu and Zhu Yingxin, water vapor evaporation requires heat absorption; the heat absorbed (sensible heat) comes from the air. Since the air loses heat (sensible heat), its temperature should decrease. Then why is it still considered a constant-temperature humidification process? Please explain. Thank you