Hi
The xbox 360 is a SMPS appliance (Switched Mode Power Supply) which means that they make one unit and send it all over the world for sale, they just drop a different adapter in there when they close the wrapper at the factory in Thailand or china, this means that the xbox is designed to work in Europe, the UK , the USA and Africa/middle/far east on power supplies ranging from 90volts 60Hz to 270 Volts 45Hz (every country has a little different supply voltage/frequency due to reasons of transmission lines and how modern power stations/substations are as well as the electricity supply companies engineering and financial choices.
Using a step down transformer in Europe for your xbox will only cause damage as they usually alter the frequency as well as dropping the voltage down, this is part of the power factor correction design as non smps appliances such as lamps or hairdryers would take more of a power surge at higher frequency and burn out quicker, in the old days (up until about 1995) smps had to be swithced by a manual red plastic switch on the back of appliances and you had to be careful which way to set it, this is now automatic and happens in under a second inside 95% of appliances, so I could take my laptop charger or my DVD player over to the USA on holiday from Scotland and it would work fine using a 2 pin plug... use a local plug and no transformer and it will stop overheating and stop shutting down. (UK power supply is 220Vac and 50 Hz, in some office and Hotel buildings, the Electricity board give them +10 % for efficiancy to make appliances run sweeter, but they burn out quicker, this is 242Volts and they bump it to 52Hz, good for aircon and lighting) in the USA the supply voltage is 110Vac and 60 Hz (60 cycles per second)

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Most problems I see happen cause the xbox is in a sleeping position. Try putting the xbox on its side, it cools easier and reads games easier(for me anyway)

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i called tech support and finally got them to take it back and fix it under the extented warrenty thing. after talking to like three different people, one dude finally asked me if i have ever had the three red lights or just one red light. i have had both several times, but it always cleared when i reset it. he then told me that the 360 kept a log of every time it has an error and since i have experienced these problems, the warrenty would cover its repair cost. sucks you had to buy a new one. if you have had red lights in the past, then i would try calling them back and letting them know and then you could have two. one for each kid.

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i did so, no change
tried unplugging and reconnecting everything.

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