Keep in mind that air conditioning moves heat from inside to outside, at a specific rate as per the BTU capacity of the system. It's constantly fighting against the heat load that's generated inside the house by cooking, lights, use of appliances (hair dryer, etc.) and electronics (computers generate heat) ... and heat that radiates in through walls and roofs heated by sunshine, windows, doors, etc. Other variables are involved such as humidity levels (squeezing moisture out of the air requires removing heat but the effective temp of the air doesn't drop ... latent heat). Units are sized to exceed the heat load under "normal" conditions so the temp inside the house can be reduced. There's a "balance-point" at which the indoor temp holds steady, the heat load exactly matches what the system can pull out. If the heat load exceeds the unit's capacity, as may happen during extremes of weather, the indoor temp will increase, although it will still of course be cooler inside than out. Setting the thermostat cooler will not have an effect in that situation ... it won't make the system run "harder" to remove more heat*, the system is either ON and removing all the heat it can, or it's OFF and removing none. A way to determine if the unit is functioning within normal limits is by checking the intake air temp (at the filter grill) and the output air (at the closest register). There should be a reduction in temp of about 16F to 20F ... which is the heat removed as air flows through. If the differential is less than 15F (more or less), then there may be a problem. Checked mine (5-ton, 60,000 BTU system) a few mins ago, 78F in, 57F out. *Except maybe in the case of a two-speed system if it's running on low speed and setting the thermostat cooler triggers it to high speed ... but in such a situation the system would likely already be running on high speed.

Yes, Sophie, that's very helpful! So I am calling it a sill but it's actually the stool; and the wood one that was removed is notched just like in the above diagram with an apron below. So it is the stool I want made of granite but I need a way to attach it without needing and apron. My DH said maybe the idea of the fabricator drilling countersunk holes in the back may work (thanks, Mama goose_gw) if he can then attach pins to the sill from underneath to slide and glue the granite on to. We would probably still use a bullnose tile underneath the granite for some extra support. Unless someone else has another idea?

8' 10" is probably fine. A bank of same-sized windows that runs into the corner & wraps with the doors will look okay, even if not centered in the room like a single window unit should be. Costs -- probably much more expensive than your current window unit. But the cost would be worth it, IMO. You'd have a dramatic view that would add value to the house, and the style would look better than the perfunctory 2 double hungs with picture unit in between. If you can use stock window sizes, that would help

A window unit type put in the wall may leak into the room if it is not angled right for drainage....or the drain line might clog up with dirt, leaves, pollen, an insect's nest....just sayin'. From experience. I had an ac unit get clogged up with a bird's nest and it drained into the room....all over the floor and curtains. And it wasn't just a drip or two...it was inches. Before I could get someone out to clean it, I had to put a baking pan underneath it to catch the water and I had to dry out the carpeting with a fan. Not fun. So I would suggest putting nothing underneath an ac unit that would get damaged by water.