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I have read through your question and would like to tell you that stiffness and numbness in the thumb can be caused by a number of conditions. The most common cause is a nerve compression or pinched nerve.
Carpal tunnel syndrome also causes numbness in the thumb. A thorough clinical examination can rule this out.
I would also advise you to get a few blood investigations done like blood sugar, blood uric acid, and ESR (erythrocyte sedimentation rate).
If your job profile involves keeping your hand in one position for too long it can be a cause. Whether you have any history of injury to the same hand in the past? You mentioned that it becomes better on applying hot water. Do you notice any bluish discoloration of the fingers?
If all the above tests come clear then we have to look for neurological causes of your problem.
For more information consult a family physician online --> https://www.icliniq.com/ask-a-doctor-online/family-physician