Burning feet....???

1) try the epsom salt soak before bed.

2) look at Biofreeze gel (or other form), to take the burning out
temporarily...at least to sleep. Amazon has it now affordably...at one time only chiros or PT had it, for more money. It has generalized down to other suppliers now. It is really really good for burning. And I've tried many things.

3) if your burning gets red, and is mostly in the toe area, try a 7 day Lamisil treatment for fungus. Many fungus infections remain below the skin level in the deeper skin layers, and will activate the burning even when you can't see any lesions or flaking of Athlete's foot. It is worth a try to do a treatment over the whole area (you don't need to gob it on), every night.
Put the cream over the tops of the toes, inbetween and underneath, and some on the instep a bit.

4) some foods will cause more burning in some people:
MSG food additive

nightshade veggies --potatoes, tomatoes, peppers, paprika, eggplant, will do it and sometimes with a delayed reaction.

Histamine releasing foods... fermented, beer, wine, pickles, etc
http://www.michiganallergy.com/food_and_histamine.shtml

5) if your feet are cold alot, they will burn when they warm up.
That is the blood returning to the cold feet stimulating the heat receptors.

These are all things I've researched over the years for night-time burning of feet. Somewhere in there is your trigger perhaps?