The "split" in a split system air conditioner is a physical one. It's split into two connected sections: the wall-mounted section inside your home and the outside section. There's another split that the system offers, and that's the temperature of the air that it blows into the room. A split system air conditioner offers both heating and cooling options, which is a very handy fact to remember when your system starts blowing suspiciously warm air into your home.
Manual Adjustment
Sometimes this discrepancy is the simplest of problems with the simplest of solutions. Has someone manually adjusted the desired temperature? If so, make the necessary adjustments to the remote control and get back to enjoying chilled air.
Accessing the Filters
When the temperature setting is correct, yet the wall-mounted unit continues to blow warm air into the room, you have a more serious issue. It may not be especially serious just yet, and you need to think about when you last cleaned the unit's filters. The wall-mounted unit should have a large hinged panel that pivots upwards. Once opened, the filter should be visible, and it may be visibly dusty.
Cleaning the Filters
You can start by vacuuming it in place, and then remove it (it should snap in and out of position). Take it outside and give it a shake to remove residual dust. It now needs to be gently washed in warm, soapy water and allowed to dry. It can then be reconnected to your AC. How does cleaning a filter help an inconsistent thermostat setting?
Air Flow
Dirty filters lead to impeded airflow, which can cause the unit to overheat, creating an obvious outcome—the unpleasantly warm air that's being directed into the room. Cleaning your unit's filters (which should be a regular part of the unit's maintenance) can make a big difference, yet the problem could persist, indicating a potential issue with the valve that determines whether the unit produces warm or cool air.
Reversing Valves
Whether the unit heats or cools is regulated by a component called a reversing valve, which is controlled by a mechanism that switches between these two modes. The production of hot air when the thermostat is set for cool air suggests damage to the reversing valve or its switch mechanism. There could also be a refrigerant leak in the unit, meaning that the gas it relies upon for its cooling function has been depleted.
Basically, if the thermostat's settings haven't been changed, and the unit's filters are clean, the problem requires a professional assessment—sooner rather than later. The more you attempt to operate a unit with a damaged heat pump or a refrigerant leak, the more operating stress the unit will experience.