hello my name is XXXXX XXXXX X am an authorized Meile service tech and I can help you today.
Yes, there is an auto reset thermostat in the back or in the grill above the oven that will trip if the oven gets too hot. And if the thermostat trips it will kill power to the oven both bake and broil will not work.
You will need to pull the oven out and remove the back panel and search for the thermostat. It is usually located next to the fan motor and will look like a small circular switch with two wires going to it.
some thermostats will have a small red or black button in the middle that if pushed will reset the switch. you will need to push hard to reset it.
if you find that then push the button in and try it out again. if it works fine and heats fine then that was all you needed to do. but if it doesn't work then I would check it with a meter on continuity. if the thermostat has continuity then you need to check power to the elements in a bake or broil cycle to see if the computer is sending voltage to the element.
if no continuity then you need to replace the thermostat.
check that out and get back to me here if you have any other questions and I will help you more.
I am sure you will find that the thermostat will be the problem since you were running the self clean cycle at high temps and now both the bake and broil to the oven don't work. It is the thermostat that causes this failure about 80% of the time.
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Thank you and please let me know how you make out with this machine.