Burning in the heel bone/Achilles Tendon can be the result of the Piriformis Syndrome[]
Case History Presentation of Piriformis Syndrome
http://rothbartsfoot.es/CaseHistory.html
Reference
Rothbart BA, Esterbrook L, 1988. Excessive Pronation: A Major Biomechanical Determinant in the Development of Chondromalacia and Pelvic Lists. Journal Manipulative Physiologic Therapeutics 11(5): 373-379.