You can have a programmable thermostat installed that allows the tenant to set the AC so it comes on several hours before they arrive home. An AC unit is not designed to provide instant cooling through out the space, but to maintain a constant temperture. If the AC is set high or off during the day, it will take hours to get to a comfortable temperture. Most will drop a conditioned space around 1 degree or more per hour in our Georgia humidity and high tempertures. A programmable thermostat is more energy efficent in operating the AC unit also.
Your local Power Company has information on the proper temperture settings that you can give to the tenant.