What causes painful burning bones sensation in my thumbs?

Difficult to say: If you having increasing pain, swelling, or the skin is turning red you should see a doctor. They can also check for things like Reyanauds. http://www.mayoclinic.org/diseases-conditions/raynauds-disease/basics/definition/con-20022916

Arthritis: Two common causes for pain in your joints would be osteoarthritis or rheumatoid arthritis