Hi there, i'm not sure if your question was meant to land in the MS community or not, but if your mother's legs are feeling hot and then cold it really could be a vascular issue like poor blood circulation....treatment depends on the cause, there is no reason to think there isn't a way that will help relieve your mothers leg issue but she needs to be diagnosed by her doctor first!
I would suggest you encourage her to see her doctor to find out what is causing this, but please keep in mind she is a grown woman who makes her own medical decisions and is likely to seek medical attention if and when she feels it's necessary, regardless of what anybody else, including her daughter, recommends.
Also be mindful that 'IF' you personally start to find your own concerns start escalating the more you google medical issues, you might need to consider there can be a negative impact to anyone's mental health with medical related googling, so it's always a good idea to stop your researching if it starts to make you feel anxious, afraid etc
Hope that helps.......JJ