My wife has stage 2 AD and is exhibiting more recognizable symptoms every day! She is 83 and cold all the time. What can I do for relief?

My husband was cold year round as well, and I am more hot natured. I told him that he can always put more clothing on, but I can only take but so much off, so he either wore a hoodie(with the hood up tight around his head)or a winter cap on his head along with either sweat pants or flannel pajama bottoms all year long. He also stay covered under at least one blanket and sometimes two.
You may just want to try bundling her up more, so you don't have to be sweating in your own house, as that's really not fair to you, when she can just put on more layers. Good luck and stay cool!

I think Dyson and DeLonghi make portable standing room air conditioners, which may be easier to manage and you can probably order them for home delivery from Amazon or HomeDepot (for small rooms). Can she spend some time outdoors (in the shade) to warm up?

Also, since you mentioned she is showing more symptoms "every day"... dementia doesn't really work that fast so I'd take her to the Urgent Care and have her checked for a UTI. If she has a fever, she may be having the chills from it. Elderly women get a lot of UTIs and often don't have physical symptoms except ones that mimic dementia (confusion, personality and behavior changes, delusions). These changes are usually described as "sudden". People with dementia are less able to express what they are feeling so don't depend on her to tell you accurately what's going on with her body. Antibiotics will clear up an infection. If left untreated it can turn into sepsis, which can be life-threatening to someone her age.

Poor circulation as well as certain medications can make a person feel cold.
My Husband also wore a coat and often gloves and said he felt cold.

Fleece type pull on pants and tops will help make her feel warmer.
Putting a hat on will also make her feel warmer (a lot of heat is lost from the head)
I'm with her about fans! I hate air blowing on me. But I do have ceiling fans but I run the so they direct air up so I do not have the air blowing on me. It still circulated the air I figure that is the important thing. There are fans with no blades so it does not look like a fan (rather expensive but it it helps it might be worth it for you)
You also might want to think about switching to another bedroom if there is one. You can adjust the temperature so it is more to your liking. A window AC unit and that can be your retreat so you don't have to go to the basement.