It seems to be quite a common problem in dementia. I think the part of the brain that controls body temperature goes wrong , either in the way it interprets signals from the nerves that indicate extermal temperature, or the internal regulation itself goes wrong. It's all controlled from within the brain and that's the part that dementia damages
Worth getting your gran checked out though - she could have a circulatory problem. Have you checked her hands and feet. If they are actually cold then your gran has a problem with her circulation, not enough blood is reaching her extemities.
Elderly people do feel the cold more - they have a thinner layer of protective fat to act as insulation, their muscles are smaller and they tend to be immobile so they don't generate heat that way - movement creates heat in muscles, improves heart action and pushes blood out to the extremities; that's why exercise makes you feel warm.
It is also absolutely true that women feel the cold more than men, despite a thicker lay of fat - they have more "cold sensor" nerves and are more sensitive to cold.
You need to be careful with the fire - if your gran's hands and feet are numb and cold due to circulation she could burn herself quite badly without realising it. Also keep an eye out for chillblains. My grandmother always felt the cold and would roast her feet as close as possible to the bars of an electric fire unless we stopped her. Several times she almost set fire to her slippers and boots but she could not feel it. She did get chillblains too.
People who suffer from extremes of lack of circulation to their hands and feet may have Reynauds - there are two forms, both have the same symptoms, which is a sudden shutting off of blood supply. This is a normal response to cold, but in Reynaud's it is very exaggerated and provoked by slight drops in temperature, or even stress. Reynaud's Disease is where the person has just the symptom but with no known cause; Reynaud's Syndrome happens where there is an underlying disease that causes it.
An electrically heated footwarmer may be better than the fire. They use a gentler, constant heat and it is almost impossible to burn oneself with it.
But I'd suggest a checkup by her GP - it;s easy to dismiss something as the dementia, and whilst it is the likely culprit there are other causes that need to be eliminated.