Stainless steel is make of iron/chromium alloy. The chromium content is usually 10%.
When you heat the knife, iron reacts with oxygen in the air to give iron oxide which shows up as rust spot. The chromium reacts with oxygen in the air to give chromium oxide which appears to be black.
There are no ordinary way to restore the knife, because iron oxide and chromium oxide can not be converted easily to iron and chromium in its original alloy form.
One possible solution can be to carry out an electrochemical process where the iron oxide and chromium oxide can be reduced back to iron and chromium (but not necessarily in its original alloy form).
Yes you make the peice of steel (a knive in this case)complete an electrical circuit.
The electrons (from the electricity) will reduce the iron oxide and chromium oxide back to iron and chromium.