Does denervation on palm of hand heal on its own?

Depends. If the nerves need to re-spout from the neck down to the palm (because the nerve axon it self has been destroyed) it can take months (so long as scar tissue does not block the pathway back to the skin, sweat glands etc. Sometimes local damage to myelin insulating the nerves can be repaired by the surviving oligodendrocytes. This usually takes less time to occur. (weeks).