If you’re purchasing from a big-box store, you can expect to pay approximately $120-$1,000 for a window unit. Window units are appealing for their quick setup and relatively low cost, but they can use more energy over time than central air and only cool the room in which they’re installed. The price will vary depending on the type of air conditioner you buy and its cooling capacity. Window units, which require minimal installation, are one of the most affordable options on the market. Portable air conditioners don’t have the cooling power of a window unit, but they do have the perk of being transportable from room to room. Expect to pay between $225 and $800 for a portable air conditioner, on average. The cost of an air conditioning system with coils, condenser and line (not including installation or ductwork) can range from approximately $2,000 to $4,000 or more. If you don’t have (and don’t want to put in) ducts, a ductless mini-split air conditioner is a good option, although pricey up front. Pricing can range from $650 to $4,250 per unit on average; you’ll need one unit for each room in which you want temperature control.
If the AC doesn’t turn off, it may be time to clean the condensing unit. Dirty condenser coils won’t give off heat efficiently and will keep the unit running.  Another possibility: The contacts on the outdoor run relay may have welded together—something that can happen over time because of frequent electrical arcing at the relay. Before checking the run relay, turn off the power to the furnace and the condensing unit. Next, disassemble the relay and pry apart the contacts. This should do the trick until you buy a replacement—which you should do soon.
Wiring up the thermostat is usually pretty straightforward if an old one is being replaced. If a thermostat is being put in where one had never been before, that could involve running new wiring. The placement of the thermostat is also important so that its sensors can get an accurate reading of the temperature. A thermostat that is blocked by a bookcase or other large furniture will not get a good reading and will not perform efficiently.
Indoor Coil -- The indoor coil is a heat transfer device. It absorbs the heat from the inside of the house and passes it on to the refrigerant and is pumped outside. Dust that builds up on the coil can hamper its ability to absorb heat. High heat transference coils use very thin metal. Airborne chemicals can cause corrosion which leads to leaks. The constant vibration of the compressor can also cause solder joints to weaken and leak. An indoor coil may operate for weeks with a tiny leak, and you may not notice the loss in performance right away. As soon as a leak is made known, it should be replaced or repaired immediately.
If you’re anything like most of our readers, you’ve spent hours online researching HVAC information in preparation for replacing your old heater or air conditioner. I’m the same way; it’s a big investment! You may want to consider saving yourself some time and money by getting an HVAC-Facts Report from this online HVAC installation cost calculator.  Take a look:

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