I inspected the bake element and found a damage on its surface. It was good evidence, that the problem is inside the bake element, not in the regulator.
It was easy to find a new bake element at Appliance Parts Pros's web site and place an order. It came in time and it took about 15 minutes to replace the broken element. The key point here was that screws due to long stand in high temperature were stocked and a screwdriver was not able to turn it. I hit them pretty hard by a hammer a couple of times and then a screwdriver was able to go.