What happens to salinity in a warm area with a lot of evaporation?

Salinity of a body of water will increase with evaporation, because the salts do not evaporate.

If a river supplies water to that body of water, than salinity might reach high values without the body of water drying completely. An good example would be the Dead Sea, witch has high salinity as the Jordan River constantly supplies it water and a little amount of salt. The water then evaporates in the desert heat while the salt accumulates in the sea.

Otherwise, without a river, a lake or sea will slowly shrink as it evaporate with its salinity increasing until it dries out totally leaving a salt lake behind. An example of that is the salt lake in the Death Valley.