Xbox 360 S suddenly freaking out and overheating whenever it's turned off?

Hello, first it's a pleasure to be able to help you today.

My name is welcome to the community.

Hello [KurtKurt], based on your description this may be happening because the console is not being cooled properly, i.e. the processor is not cooling as it should be.

I don't know how long it has your Xbox 360 and neither is the state it is, but this can happen by the accumulation of dirt inside the console, so it does not and cooled properly and also the thermal paste of the processor can be very dry and not be cooling the processor as it should.

Could it be overheating?

I had a similar problem with my 360 years back, would make a strange whirring noise then switch off. Turned out to be overheating.

My XB Elite began overheating this past weekend after having gone almost 3 years of it NEVER overheating. I'm not sure I received this update but I can't check because whenever I turn it on, it spins up and goes to the 2-light Ring of Death. I don't want
to spend time on the phone w/MS or give my CC# out. My first thoughts were about an Update I got late last week (5-19ish). you are the first person to state they suddenly began having overheating issues.

Your router may be overheating. If there's too much traffic and it's a rather cheap router, it'll overheat, or just freak out and disconnect. Too many devices on a network can cause this. Your Xbox 360 just might me the straw breaking the camel's back

If your Xbox One or Xbox One S keeps TURNING OFF, it is most likely due to OVERHEATING. Turn on the console – Scroll left from
Home to open the guide – Select Settings – Select All Settings – Select Power – Select Turn off or restart