Burning sensation in the soles of feet may be due to Diabetes mellitus, Vit B12 deficiency, liver disease, hypothyroidism, usage of certain drugs, nerve compression, Peripheral vascular disease (narrowing of blood vessels). Sacralization of L5 also may cause burning sensation, but will not be prominently noticable.
You may get yourself tested for the above diseases if your probblem is severe. Please stop smoking, if you are a smoker. Do get back for any other queries.
If neuropathies have been ruled out then peripheral vascular diseases should be ruled out. The chances are more if there is a long history of smoking. It is also important to make sure that arch supports are of the right fit.