Hi
Welcome to the MedHelp forum!
Burning sensation or heat in the feet with or without numbness can be due to plantar fasciitis, diabetes, Sjogren’s syndrome, peripheral neuropathies, hypothyroidism, SLE, alcoholism, peripheral artery disease, sciatica, sarcoidosis, amyloidosis and high blood pressure. I think you should discuss these possibilities with your doctor. It is difficult to comment beyond this without examining. A comprehensive investigation (blood tests, nerve conduction studies and dopplar studies) is required keeping all the points in mind.
Hope this helps. Please let me know if there is any thing else and do keep me posted. Take care!