I am experiencing the same thing, and sadly I am only 22 years old (male). My symptoms are in my right foot and I get this burning/hot feeling in my foot. It lasts only for a few moments and then vanishes. There is no warning for it and happens, on average, at least 30 times a day for me.
I'm an IT technician so I'm skilled with computers, and after doing comprehensive research on the Internet I discovered 3 possible causes for having hot flashes/burning sensations in your feet.
1) Venous Disease - Basically, you could have a blood clot in your legs that could be causing the problem. If you are also noticing reddish spots or spider/Vericous veins on your ankles then this is most likely the problem. Swelling of your feet or ankles is also a symptom.
2) Diabetic Peripheral Neuropathy - Yes, it's true, this problem could be a result of Diabetes. According to my research, Diabetic Peripheral Neuropathy can cause your nerves to misfire, and as a result cause you to feel a burning pain/hot flash in your foot. The best way to treat this is to treat the diabetes. If left untreated you could suffer worsening pain as a result of the nerves misfiring.
3) Peripheral Neuropathy - Same as above except not related to diabetes. Peripheral Neuropathy can be caused by other diseases and problems in your body.
IMO, if you are overweight and/or generally unhealthy (like I am), then I would look into numbers 1 and 2 as these would most likely fit your classification.
If you consider yourself to be generally healthy and in good physical condition then I would look into number 3 and try to find other reason as to the cause of your Peripheral Neuropathy.
Hope this helps!