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I have learnt that heat exchange between systems occurs when the temperature of the systems differ, but in case of evaporation, the process creates a cooling effect even in an isothermal condition (between the evaporating liquid and the surrounding).
Is evaporation possible as an isothermal process? If so, how is there heat exchange even in an isothermal process?
The concept is evaporative cooling. Essentially a liquid does work on the environment by expanding itself, thereby lowering its own internal energy.
This expansion is made possible by the fact the the liquid can convert itself into gas. The particles that manage to do this are on average possessing more KE than the other particles (remember that particle KE are not uniform but follow a Boltzmann distribution, and only particles with enough KE to break intermolecular bonds can become gas), in other words evaporation causes the remaining liquid to have on average, lower KE particles (a drop in temperature). Necessarily the particles that managed to escape are at the appropriate higher temperature, and as a result expand the volume they take up (do work) until back in thermal equilibrium with the liquid or environment or both. The result is both the liquid and it's vapor blanket being a lower temperature than before being exposed.
If there is zero convection of this vapor then net evaporation eventually stops (condensation of the vapor back into the gas liquid interface equals evaporation) and the cooling effect ceases. if the whole shebang is enclosed in fixed volume then temperature as well as pressure will increase (heat is from environment) until all the water and water vapor is at environment temperature. The gas pressure of this vapor is know as the vapor pressure, which is dependent on temperature.
In reality, convection is non zero. There are breezes, and warm vapor rises away on its own, creating more opportunity for the liquid to vaporize and continue losing energy by losing its fastest particles to the environment. Exposed water bodies are typically a few degrees below air temperature because of this.
Cooling effect doesn't necessarily mean fall in temperature.
For example, if I have 1 mole of water at 273 K, some 0.3 moles can spontaneously evaporate, producing water vapor at 273 K, thereby forming ice at 273 K from the rest 0.7 moles.
(NOTE: values are not actual ones, just for explaining this example).
Now you can see that this process is isothermal, but part of the water which evaporates produces a "cooling effect" on the rest, ultimately freezing it.
Also note that the process i described above might not be spontaneous practically, in terms of entropy change and change in Gibbs' free energy
If an empty pan is put on the stove and a natural gas flame is placed under the pan, the pan will heat up to the flame temperature of 1083 C. This will probably destroy the pan. On the other hand, if pure water is placed in the pan, the pan will heat up to slightly more than 100 C at sea level, as the heat being put into the pan by the flame boils the water rather than heats the pan. Thus, this process is isothermal because the pan doesn't change temperature as heat is added. This isothermal condition will continue until all of the water is boiled out of the pan, which will then increase in temperature to 1083 C. In a sense, the boiling of water is a cooling process, even under isothermal conditions, because the pan is kept far below the flame temperature as long as boiling is occurring.
