Ductless heat exchanger

Also known as mini-split cooling/heating system or air-source ductless mini-split or simply heat pump, this Klimaire (model KSWG012-H113) falls in the category of HVAC (Heating Ventilating & Air Conditioning) but doesn't really ventilate because it's ductless. It recirculates room air, blowing it downwards after either heating or cooling it. It takes whatever heat is in the outdoors air to warm the room, and vice versa to cool it.
The recommended mounting height is actually 91 inches above floor, but this model has controllable vanes for near-horizontal air flow, and the climate here needs more heating than cooling, thus the below-window mount. The required hole size for the bundle of tubes and wires is about 3 inches diameter -- best to use 2x6 studs if you're drilling through the bottom plate (which is what I did to preclude moisture problems associated with going through the wall).

Both indoors and outdoors unit are fairly quiet. At 12,000 Btu/h (1 ton), this model is rated at 13.1 SEER (cooling) and 7.7 HSPF (heating). It requires just a standard 120V 60Hz circuit, whereas the next larger size requires 220V.

$784 Klimaire unit, after delivery & tax
$19 misc. hardware
$385 connection by HVAC pro
$1188 TOTAL COST
(free planning, design and mounting by owner as usual)